The defendant and his partner, both Springfield police officers, stopped a car containing three farm workers of Mexican heritage because, in the words of the defendant, “Mexicans typically don’t drive with a license and they typically drink and drive.” The driver could not produce a license but did produce the car’s registration. One of the passengers in the back seat produced a Mexican driver’s license. All three men were removed from the car and their wallets were taken. *461The defendant searched the car and its contents and, by his own admission, also looked through the wallets.1 The men were then allowed to return to the car and drive away.2

These events occurred shortly after the workers had received and cashed their paychecks, and each man’s wallet contained more than $450. Once permitted to return to the car, the men discovered that almost all the cash had been taken. They quickly reported the matter to the police, and a jury convicted the defendant of three counts of larceny over $250, G. L. c. 266, § 30.

The defendant raises several issues on appeal, only one of which merits discussion at any length.3 Specifically, the defendant argues that he should have been allowed to bring out on cross-examination that the victims were undocumented immigrants and that they were not in proper possession of Social Security numbers. He contends that this line of questioning would have shown the victims’ bias and undermined their credibility. The trial judge prohibited the questioning, reasoning that it was irrelevant and that the witnesses could not be impeached by prior bad acts unless they resulted in a conviction. We agree with the judge.

The defendant’s argument is built on what he calls the absence of proof that the victims were legal residents of the United States. This argument’s premise is incorrect; the Commonwealth was not required to establish the immigration status of the victims before they could testify. With certain exceptions not at issue in this case, “[a]ny person of sufficient understanding . . . may testify in any proceeding, civil or criminal, in court or before a person who has authority to receive evidence.” *462G. L. c. 233 § 20. The victim of a crime need not be a citizen or a legal resident of the United States in order to testify in our courts.

Just as legal residence in the United States was not a necessary qualification in order for the victims to testify, their immigration status was not relevant in this case. “ ‘Relevant evidence’ is evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more or less probable than it would be without the evidence.” Mass. G. Evid. § 401 (2011). Commonwealth v. Schuchardt, 408 Mass. 347, 350 (1990). We perceive no fact at issue in this case (nor has the defendant pointed us to one) that becomes more or less probable depending on the victims’ immigration status.

The fact that information is not probative of any fact at issue does not necessarily mean that it cannot be used to impeach a witness’s credibility or to establish bias. “[Ejvidence of bias is almost never a collateral matter.” Commonwealth v. LaVelle, 414 Mass. 146, 153 (1993). “The right of a criminal defendant to cross-examine a prosecution witness to show the witness’s bias, and hence to challenge the witness’s credibility, is well established in the common law, in the United States Constitution (Sixth Amendment), and in the Constitution of the Commonwealth (art. 12 of the Declaration of Rights).” Commonwealth v. Tam Bui, 419 Mass. 392, 400, cert, denied, 516 U.S. 861 (1995). However, a defendant’s entitlement to attack credibility or to establish bias does not justify an otherwise impermissible appeal to prejudice. There must be some plausible connection between the information the defendant seeks to introduce and the witness’s credibility. See id. at 401 (tenuous theory of bias properly excluded). No such connection exists here.4 There is no reason to believe that the fact that the witnesses may not have been legally resident in this country made them any less likely to be truthful. If anything, their insecure legal status would likely make them less inclined to turn to law *463enforcement officials for help. See Commonwealth v. Morgan, 449 Mass. 343, 364 n.17 (2007) (fact that witness was aware that he might be subject to prosecution for illegal entry into the country “adds nothing” to the discussion of bias).

The trial judge was equally correct to prohibit the defendant from cross-examining the victims about allegedly providing false information to obtain Social Security numbers. “Generally, a witness cannot be impeached by use of a specific act of misconduct not resulting in a conviction.” Commonwealth v. Podkowka, 445 Mass. 692, 696 (2006), citing to Commonwealth v. Bregoli, 431 Mass. 265, 275 (2000). See Mass. G. Evid. § 608(b). There was no evidence here to suggest that the victims had been convicted of any crime related to the use or obtaining of Social Security numbers. Indeed, the defendant has not even placed anything in the appellate record to demonstrate that the victims were not in proper possession of Social Security numbers or that they provided false information to obtain them.

Judgments affirmed.