After a jury trial on an indictment charging murder in the first degree, the defendant was convicted of murder in the second degree of Celestine Walker. He also appeals his conviction of violating a G. L. c. 209A abuse prevention order.2 On appeal, he claims his motions to dismiss and to suppress were improperly denied, improper bad acts were admitted in evidence, and that he was improperly denied a Bowden instruction.3 We affirm.

1. Motion to dismiss. The defendant claims that the motion judge should have allowed his motion to dismiss the indictments because the omission of Ashia Reese's prior statement to the police impaired the integrity of the grand jury. We disagree.

Reese told the police that she drove the victim and the defendant to the victim's apartment on the night of May 11, 2013, that she saw them walking towards the apartment where the victim lived, and that she did not actually see them go into the apartment. In the grand jury, Reese testified that she saw the defendant and the victim walk towards and enter the victim's building, but she did not see them enter the apartment itself.

Although the prosecutor did not present Reese's police interview to the grand jury, this did not constitute withholding exculpatory evidence. As the motion judge properly found, Reese's grand jury testimony was "consistent, in material respects, with her earlier statements to the police that she drove the victim and the [d]efendant to the victim's apartment on the night of May 11, 2013." Even though Reese told the police that she did not see the defendant and the victim go into the victim's apartment, and then told the grand jury that she saw them enter the building, this was consistent since she was responding to two different questions: the first being whether she "saw them actually get into the apartment," and the second being whether she saw them "go into the building." As the motion judge found, this is far from proof that the prosecutor knowingly or recklessly presented false or deceptive evidence to the grand jury, nor is there proof that this was presented for the purpose of obtaining an indictment. See Commonwealth v. Mayfield, 398 Mass. 615, 620-622 (1986).

Rather, the Commonwealth provided the grand jury with a compelling case that identified the defendant as the individual who killed the victim and provided sufficient probable cause to arrest the defendant for murder. See Commonwealth v. McCarthy, 385 Mass. 160, 163 (1982). The defendant has failed to show that the difference in Reese's statement probably influenced the grand jury's decision to indict. Indeed, it should be noted that the petit jury heard the audio recording of Reese's prior statements to the police, and they still found the defendant guilty beyond a reasonable doubt. See Commonwealth v. Trowbridge, 419 Mass. 750, 754 (1995).

2. Motion to suppress. The defendant also claims that the motion judge erred in denying his motion to suppress the allegedly coerced statements he made to the victim's children after they entered the apartment of his friend, Melva Page, on the day the victim's body was found. We disagree.

As an initial matter, the defendant's statements that "it was an accident" and that he had left the victim sleeping, were spontaneously made when the victim's children entered Page's apartment and prior to any physical contact. As the motion judge properly determined, "the [victim's] family's unwanted entry into Ms. Page's apartment is insufficient to show that the [d]efendant's statements were a product of physical or psychological coercion." Even if the defendant was surprised, that was not sufficient to establish that his will was overborne when he made his initial statements.

When the victim's children confronted the defendant, he repeated what the children had previously heard him state, i.e., that it had been an "accident." Even the defendant admits, this was an effort to "acquit himself," which the judge was free to conclude was evidence of a rational intellect and free will. See Commonwealth v. Vasquez, 387 Mass. 96, 100 (1982). While the victim's children did hit, kick, and punch the defendant while asking about their mother's whereabouts, the defendant merely repeated that "I didn't do it" and "I'm sorry, it was an accident." As the judge found, even if the defendant's mental state was affected by the physical violence, this does not automatically render his statements involuntary. See Commonwealth v. Selby, 420 Mass. 656, 664 (1995). Contrast Commonwealth v. Mahnke, 368 Mass. 662, 669-671 (1975). Also, there was no evidence that the defendant sustained any injuries during the incident, nor was there any evidence of him being in distress when the police arrived. In the end, the motion judge properly concluded that the defendant's statements were the "product of his own free will," and that he was not entitled to have them suppressed.

3. Prior bad acts. The defendant also claims that the judge erred by admitting in evidence that the defendant had choked the victim on two prior occasions because such testimony "was irrelevant to the extent it was cumulative of other evidence admitted to show motive," and "unduly prejudiced the defendant by leading the jury to believe he acted in conformity and killed the victim." We disagree.

Prior to the defendant's first trial, the trial judge held a voir dire on the Commonwealth's proposed admission of twelve prior bad acts. Four witnesses described seeing the defendant choke the victim on specific occasions or generally over a period of time. The judge exercised his discretion to admit only two of the choking incidents. Contrary to the defendant's claim, these two incidents were properly admitted to show the hostile nature of the defendant's relationship with the victim and his pattern of acting on that hostility. See Commonwealth v. Butler, 445 Mass. 568, 575 (2015) ; Commonwealth v. Oliveira, 74 Mass. App. Ct. 49, 54 (2009).

While four other witnesses testified about prior incidents of abuse, this did not render the choking incidents cumulative and overly prejudicial. No other witnesses testified to seeing the defendant choke the victim between 2011 and 2013. Furthermore, the cause of death in this case did not make the choking incidents either "unnecessary" or propensity evidence. The two choking incidents were relevant and admissible for an independent purpose (as discussed above), which was also relevant to the defendant's motive. Finally, the judge properly instructed the jury (on three occasions) on the proper use of the prior bad act evidence. There was no error or abuse of discretion.

4. Bowden instruction. Finally, the defendant claims that the trial judge erred by denying the defendant's request for a Bowden instruction regarding the alleged shortcomings of the police investigation. We disagree.

In Commonwealth v. Bowden, 379 Mass. 472, 485-486 (1980), the Supreme Judicial Court held that the "failure of the authorities to conduct certain tests or produce certain evidence was a permissible ground on which to build a defense." The error in Bowden was the judge's removal of the adequacy of the investigation evidence from the jury's consideration.

The defendant's claim that the same occurred here-in the absence of an instruction-has no basis in the record. In fact, the defendant was allowed to argue Bowden principles throughout trial. See Commonwealth v. DaSilva, 471 Mass. 71, 84 (2015). It was brought out in the defendant's opening statement, his closing argument, and through his examination of multiple witnesses. Under these circumstances, there was no error in the judge's refusal to instruct the jury on the defendant's Bowden defense. It was simply not required. See Commonwealth v. Daye, 411 Mass. 719, 740-741 (1992).

Judgments affirmed.