The defendant was found guilty by a jury of murder in violation of General Statutes § 53a-54a (a).1 The trial court rendered a judgment sentencing him to a term of imprisonment of forty years. The defendant appeals claiming that the trial court improperly: (1) limited the cross-examination of the state’s primary witness; and (2) allowed the state to cross-examine the defendant concerning prior acts of uncharged misconduct. The defendant appealed directly to this court pursuant to General Statutes § 51-199 (b) (3).2 We affirm.
The jury heard the following evidence that supports its conclusions that the defendant murdered the victim. In February, 1985, the defendant began selling drugs. In 1983, the defendant had made the acquaintance of Roberto Quinones and, in 1986, Quinones *198began selling drugs for the defendant at various nightclubs in Port Chester and White Plains, New York. Throughout 1986 Quinones and the defendant were together daily. They frequently met at the defendant’s apartment at 9 Halloween Boulevard, Stamford, to prepare drugs for sale. They roomed together in other locations while they stored drugs in the defendant’s apartment, and they went to nightclubs together. Quinones often drove the defendant to these places because the defendant did not have a United States3 driver’s license.
On September 21,1986, the body of the victim, Sylvia Hunt, a prostitute, was discovered wrapped in a rolled carpet lying near the side of Interstate 95 in Greenwich, near the Mianus River Bridge. The state police were called, secured the area and summoned the state medical examiner. An examination of the body by the medical examiner disclosed that the body was punctured by fifteen stab wounds and that the cause of death was multiple stab wounds to the chest. Blood tests revealed traces of alcohol, cocaine and morphine in Hunt’s body.
Subsequent to the discovery of the murder victim, the state police interviewed Quinones as part of their investigation. Quinones informed the police that the defendant had rented an apartment on Halloween Boulevard in Stamford from May to October, 1986. Quinones, who had been to the apartment on numerous occasions, testified that on a Saturday in September, 1986, he visited the defendant at his Halloween Boulevard apartment. The apartment had one entrance in the kitchen-living room area and another in the bedroom. Although Quinones had always used the bedroom entrance when visiting, the defendant told Quinones he could not enter that way and, on that particular day, *199he would have to use the kitchen entrance instead. That evening, after preparing drugs, the defendant and Quinones went to La Cascada, a nightclub, where the defendant told Quinones that he had killed a girl with a knife because she had been stealing his drugs and his “necklace chains.” The defendant told Quinones that he had gone crazy and “killed her like a dog.” He further stated that he had the body at his apartment but had otherwise cleaned up.
The following day Quinones returned to the Halloween Boulevard apartment to prepare more drugs. While in the apartment with the defendant, Quinones observed “a bulk in between the two mattresses” in the defendant’s bedroom. The defendant asked Quinones to find the defendant’s uncle so that the three of them could dispose of the body. Unable to locate the defendant’s uncle, Quinones returned to the apartment, where he saw the living room rug rolled and tied.
About 4 a.m. the next day, Quinones, the defendant and the defendant’s uncle drove in the defendant’s red Buick automobile to the apartment. Quinones waited while the defendant and his uncle carried the rug down from the apartment and put it in the trunk of the defendant’s car. The three men got into the car and the defendant drove to the Mianus River Bridge. Quinones watched as the defendant and his uncle removed the rug from the trunk and threw it behind the barrier alongside the highway. Quinones later identified the rug in which the victim’s body was found as the same rug he had seen the defendant remove from the Halloween Boulevard apartment and discard along the highway.4 Later that same day Quinones returned to the defendant’s apartment and saw the defendant cut *200off bloodstained portions of his mattress, place them in plastic bags, and place the bags in the trunk of his car for disposal.
The following week, the defendant and Quinones were driving by the area where the body had been left and noticed that the police had discovered the body. In late September or early October, Quinones drove the defendant to the airport, and the defendant told Quinones to give the defendant’s car to the defendant’s wife, who lived in White Plains.
One of Quinones’ neighbors testified that, after the police had found the body, Quinones had told him that the defendant had stabbed a black prostitute to death, had rolled up the body in a rug, and had disposed of the body along the highway. In January, 1988, the police seized portions of the flooring and the doorjambs between the kitchen and bedroom areas from the defendant’s apartment on Halloween Boulevard. Laboratory tests revealed the presence of human blood on some of the items.
In the fall of 1988, the police seized a red Buick parked in a garage on Oakwood Avenue in White Plains. The tenants at the address stated that the car had been left there by previous tenants, the defendant’s wife and her brother, who had moved out one year earlier. The police found a number of yarn-like fibers in the trunk of the Buick. Laboratory tests revealed that these fibers were consistent with those taken from the rug in which the victim’s body was found. The police also found a key chain bearing the initial “S” in the trunk of the Buick.
The police testified that the defendant had told them that he thought the key chain looked like one the defendant’s wife had given him.5 The police also testi*201fied that the defendant had told them that he had always kept a knife in the red Buick. He described the knife as a machete.
I
The defendant’s first claim is that the trial court abused its discretion and prejudiced his defense by refusing to allow him to cross-examine Quinones, the state’s primary witness, concerning uncharged misconduct that had occurred ten months after the murder.6 At trial, Quinones testified that the defendant had told Quinones that he had killed Hunt. The defendant attempted to establish that Quinones had killed the victim.7 The *202defendant attempted to bolster this theory by introducing into evidence the fact that, in July, 1987, Quinones had threatened to slash a former girlfriend and to kill her, her husband and other members of her family. After hearing argument outside the presence of the jury, the trial court excluded this evidence because it was too remote in time and not factually similar to the murder.
Our case law recognizes the right of a defendant to introduce evidence that indicates that another person, not the defendant, committed the crime with which the defendant is charged. See, e.g., State v. Echols, 203 Conn. 385, 392, 524 A.2d 1143 (1987); State v. Burge, 195 Conn. 232, 252, 487 A.2d 532 (1985); Siemon v. Stoughton, 184 Conn. 547, 555-56, 440 A.2d 210 (1981); State v. Giguere, 184 Conn. 400, 405, 439 A.2d 1040 (1981); State v. Marshall, 166 Conn. 593, 601, 353 A.2d 756 (1974). The defendant must, however, present evidence that directly connects a third party to the crime with which the defendant has been charged. State v. Echols, supra; Siemon v. Stoughton, supra; State v. Giguere, supra. “It is not enough to show that another had the motive to commit the crime; State v. Marshall, supra; State v. Perelli, 125 Conn. 321, 328, 5 A.2d 705 (1939); nor is it enough to raise a bare suspicion that some other person may have committed the crime of which the defendant is accused. Brown v. State, 275 Ind. 227, 231, 416 N.E.2d 828 (1981).” State v. Echols, supra.
The rules of relevancy govern both the initial presentation of third party culpability evidence, and the admissibility of particular evidence in that regard. See State v. Echols, supra, 393; State v. Burge, supra; State v. Giguere, supra, 405-406; State v. Marshall, supra, 601-602. Whether third party culpability evidence is direct enough to be admissible is ultimately a matter of the discretion of the trial court. State v. Echols, supra.
*203“We test the question of remoteness by this rule: ‘Generally speaking, the question of remoteness, as justifying the exclusion of evidence, must depend upon all the considerations, including time, the character of the evidence, and all the surrounding circumstances which in the opinion of the court ought to have a bearing upon its worthiness to be brought into the consideration and determination of the matter in contention.’ State v. Kelly, 77 Conn. 266, 269, 58 Atl. 705 [1904].” Bishop v. Copp, 96 Conn. 571, 580, 114 A. 682 (1921). The evidence in question here related to conduct that occurred ten months after the murder that arose under very different circumstances and the threat was made to different individuals. Furthermore, there is no connection between Quinones’ former girlfriend and the murder victim. Compare State v. Burge, supra, 252 (third party had confessed to recent commission of similar assault); State v. Ross, 18 Conn. App. 423, 424, 429, 558 A.2d 1015 (1989) (third party had been involved in similar fight one week earlier and had argument with victim moments before shooting). Under the circumstances, the trial court did not abuse its discretion in concluding that this evidence was not relevant because it was too remote in time.
Furthermore, the trial court found this evidence factually dissimilar to the circumstances surrounding the murder. The defendant agreed with the trial court’s determination that this case does not involve a signature crime.8 Additionally, the trial court properly excluded this evidence because it did not directly connect Quinones to the murder. We conclude that the trial court’s ruling was not an abuse of discretion.
II
The defendant’s second claim is that the trial court improperly permitted the state, in cross-examining the *204defendant, to go beyond the scope of the direct examination of the defendant. The challenged cross-examination concerned the defendant’s purported violence toward women. At trial the defendant testified on direct examination that he had many relationships.9 He portrayed himself as a popular, churchgoing man who had romantic relationships with many women.10 *205Although some women were jealous of his popularity, their jealousy was expressed in harmless ways.11 The defendant also portrayed himself as a peaceful man; he claimed often to have stopped fights Quinones would get into and he claimed not to have fought with Quinones even when he was angry with him.12 On cross-examination, the defendant testified that he believed his relationships with women were good but that some women would fight with him. When the state tried to question the defendant about his relationship with a specifically identified woman, the defendant objected.13
*206With the jury excused, the court heard argument on the prejudicial effect of the anticipated testimony concerning an alleged attempted sexual assault accompanied by physical violence. The state claimed that the defendant had portrayed himself as having good relationships with women and that the state, therefore, was entitled to pursue the matter further.14 The court held that the alleged sexual assault was not relevant to a murder by stabbing and the prejudicial effect of the testimony on this topic outweighed its probative value. The court held, however, that testimony regarding alleged physical violence against the woman was admissible. The defendant had opened the door to this testimony when he created an impression of himself as a peaceful man with good relationships with women.
“Generally, a party who delves into a particular subject during the examination of a witness cannot object if the opposing party later questions the witness on the same subject.” State v. Graham, 200 Conn. 9, 13, 509 A.2d 493 (1986); see also State v. Roy, 173 Conn. 35, 50, 376 A.2d 391 (1977). “The party who initiates discussion on the issue is said to have ‘opened the door’ to rebuttal by the opposing party.” State v. Graham, supra. “ ‘The doctrine of opening the door cannot, of course, “be ‘subverted into a rule for injection of prejudice.’ ” United States v. Lum, [466 F. Sup. 328, 335 (D. Del. 1979)], quoting United States v. Winston, [447 F.2d 1236, 1240 (D.C. Cir. 1971)].’ State v. Glenn, [194 *207Conn. 483, 499, 481 A.2d 741 (1984)]. The trial court must carefully consider whether the circumstances of the case warrant further inquiry into the subject matter, and should permit it ‘ “only to the extent necessary to remove any unfair prejudice which might otherwise have ensued from the original evidence.” California Ins. Co. v. Allen, 235 F.2d 178, 180 (5th Cir. 1956).’ United States v. Winston, supra. Thus, in making its determination, the trial court should balance the harm to the state in restricting the inquiry with the prejudice suffered by the defendant in allowing the rebuttal. Id., 1241-42; People v. Arends, 155 Cal. App. 2d 496, 509, 318 P.2d 532 (1957).” State v. Graham, supra, 13-14.
“ ‘When a witness voluntarily testifies, as did the defendant here, he asks the jury to believe him. The jury should be informed about the sort of person asking them to take his word.’ State v. Staples, 120 N.H. 278, 283, 415 A.2d 320 (1980), quoted in State v. Glenn, [supra, 498-99].” State v. Williamson, 206 Conn. 685, 699, 539 A.2d 561 (1988). “ ‘Matters which might not be strictly relevant on direct examination may be so on cross-examination where that matter is explored for the purpose of credibility. Given that function of cross-examination in shedding light on the credibility of the witness’ direct testimony, “[t]he test of relevancy is not whether the answer sought will elucidate any of the main issues, but whether it will to a useful extent aid the court or jury in appraising the credibility of the witness and assessing the probative value of the direct testimony.” ’ ” State v. Williamson, supra, quoting State v. Ouellette, 190 Conn. 84, 102, 459 A.2d 1005 (1983). A question is within the scope of the direct examination if it is intended to “rebut, impeach, modify or explain any of the defendant’s direct testimony . . . .” State v. Zdanis, 173 Conn. 189, 196, 377 A.2d 275 (1977).
*208The court has wide discretion to determine the scope of cross-examination. State v. Jackson, 198 Conn. 314, 319, 502 A.2d 865 (1986); State v. Sharpe, 195 Conn. 651, 657, 491 A.2d 345 (1985); State v. Thompson, 191 Conn. 146, 148, 463 A.2d 611 (1983); Akers v. Singer, 158 Conn. 29, 36, 255 A.2d 858 (1969); State v. Kurz, 131 Conn. 54, 37 A.2d 808 (1944). “ ‘Every reasonable presumption should be given in favor of the correctness of the court’s ruling in determining whether there has been an abuse of discretion.’ ” State v. Jackson, supra, quoting State v. Briggs, 179 Conn. 328, 333, 426 A.2d 298 (1979), cert. denied, 447 U.S. 912, 100 S. Ct. 3000, 64 L. Ed. 2d 862 (1980). “ ‘Because of the difficulties inherent in this balancing process, the trial court's decision will be reversed only where abuse of discretion is manifest or where an injustice appears to have been done.’ ” State v. Williamson, supra, 698, quoting State v. Howard, 187 Conn. 681, 685, 447 A.2d 1167 (1982); see also State v. Braman, 191 Conn. 670, 676, 469 A.2d 760 (1983). “Our review is limited to whether the trial court’s rulings exceeded the latitude accorded its discretion in such matters.” State v. Williamson, supra, 698-99.
With the jury excused, the trial court considered arguments by the parties about the proposed questioning concerning the defendant’s alleged misconduct with respect to the woman. The court agreed with the state that by portraying himself in a certain manner on direct examination, the defendant had opened the door to questions that would elicit testimony contradicting this portrayal of the defendant to enable the jury better to assess the defendant’s credibility. On weighing the probative value and prejudicial effect of this proposed testimony, however, the court determined that testimony concerning violence toward the woman would be allowed but testimony concerning an alleged sexual assault would not. Subsequently, while being ques*209tioned on cross-examination about his role as a peacemaker at the nightclub, the defendant admitted that he had had arguments with women and had slapped them around.15 Although the defendant did not state on direct examination that he was never violent toward women, the record supports an inference that his relationships were nonviolent. The trial court did not abuse its discretion when it allowed the state to cross-examine the defendant to modify this inference.
The judgment is affirmed.
In this opinion Peters, C. J., Berdon and Norcott, Js., concurred.