
628 A.2d 664 (1993)
STATE of Maine
v.
Edward C. ROBINSON, Jr.
Supreme Judicial Court of Maine.
Argued June 16, 1993.
Decided July 16, 1993.
*665 Garry L. Greene (orally), Asst. Atty. Gen., Augusta, for the State.
Andrew J. Smith (orally), Paine, Lynch & Harris, P.A., Bangor, for defendant.
Before WATHEN, C.J., and GLASSMAN, CLIFFORD, COLLINS, RUDMAN and DANA, JJ.
RUDMAN, Justice.
Edward C. Robinson appeals from the Superior Court (Penobscot County, Beaulieu, J.) judgments entered on the jury verdicts finding him guilty of intentionally or knowingly causing the deaths of Patricia Maguire and Robert Blanchard. See 17-A M.R.S.A. § 201(1)(A) (1983). Because we find no reversible errors, we affirm the judgments.

I

Voluntariness of Robinson's Statements
The trial court initially issued an order suppressing all of Robinson's statements made to the police on June 25, 1988, obtained during a custodial interrogation without Miranda[1] warnings. Neither party contests the trial court's well-reasoned decision to suppress Robinson's statements.
The State, however, filed a motion for further findings of fact and conclusions of law seeking a determination from the trial court that Robinson's statements were voluntarily made. See Harris v. New York, 401 U.S. 222, 91 S.Ct. 643, 28 L.Ed.2d 1 (1971) (statements of accused, taken without full Miranda warnings, were admissible for impeachment purposes); State v. Durepo, 472 A.2d 919, 922-24 (Me.1984); see also Annotation, Admissibility, In Criminal Case, of Evidence for Purpose of Impeachment of Witness, as Exception to Exclusionary Rule Precluding Admission of Evidence Obtained in Violation of Federal Constitutional Rights  Supreme *666 Court Cases, 107 L.Ed.2d 1162 § 6[a] at 1169-70 (1991). The court subsequently issued an order finding, beyond a reasonable doubt, that Robinson's statements were made voluntarily. See State v. Collins, 297 A.2d 620, 627 (Me.1972). On appeal, Robinson challenges the trial court's finding that the statements at issue were made voluntarily, beyond a reasonable doubt.
The trial court's determination that the State has met its burden of establishing that a defendant's statement is voluntary beyond a reasonable doubt will not be disturbed on appeal if there is evidence in the record to support such a finding. State v. Candage, 549 A.2d 355, 359 (Me.1988) (citing State v. Larrivee, 479 A.2d 347, 349 (Me.1984)). Our review of the record discloses ample support for the trial court's conclusion.

II

Alternative Perpetrator Evidence

A. Standard of Review
The question of the relevancy of proffered evidence is reviewed under a clear error standard. State v. Dechaine, 572 A.2d 130, 133 (Me.), cert. denied, 498 U.S. 857, 111 S.Ct. 156, 112 L.Ed.2d 122 (1990). The decision whether to admit evidence, however, is more frequently reviewed under an abuse of discretion standard because the question of admissibility frequently involves the weighing of probative value against considerations militating against its admissibility. See id. (citing M.R.Evid. 403; State v. Nye, 516 A.2d 560, 562 (Me.1986)).

B. Exclusion of alternative perpetrator evidence
Robinson contends that the Superior Court deprived him of a fair and impartial trial when it refused to allow him to introduce alternative perpetrator evidence. We disagree.
At trial, Robinson made several offers of proof regarding his alternative perpetrator evidence. Specifically, Robinson told the court that he wanted to offer the testimony of Jack Stillings, Winslow Newbert and Michael Whitham for the purpose of establishing that Stillings had a motive and the opportunity to kill the victims. Robinson proffered that Stillings' testimony would establish that he (Stillings) had been dating and was intimate with Maguire shortly before her death, and that Newbert would testify that: (1) he had seen Stillings dealing in stolen firearms and part of a "stolen weapons ring" had met at Maguire's trailer; and (2) Stillings told him that: he (Stillings) had his lawyer conducting a suppression hearing to determine who was leaking evidence to the police; he was concerned about the leak, the leak had to be taken care of, that he'd been known to do it before, and that he intended to do something about the leak; he believed that either Maguire or Newbert were talking to the police; and, Maguire was a drinker who tended to talk too much when she had been drinking. Robinson also intended to ask the Court to take judicial notice of the fact that at the time of the murders, Stillings was under indictment for receiving stolen firearms and tampering with a witness.[2] Lastly, Robinson intended to present evidence to establish that Stillings had the opportunity to kill Maguire due to the fact that Stillings was seeing a woman who lived within a four-minute walk of Maguire's trailer, thus enabling Stillings to easily approach the trailer through the woods and commit the crime.
The Superior Court viewed the proffered evidence as an accusation by Newbert that Stillings committed the crime. Accordingly, the court, based on its reading of the dissent in State v. Conlogue, 474 A.2d 167 (Me.1984), refused to admit the evidence concluding that the evidence did not clearly link Stillings to the commission of the crime.
We have never required that alternative perpetrator evidence "clearly link" the alternative perpetrator to the commission of the crime at issue. Requiring that *667 alternative perpetrator evidence "clearly link" the alternative perpetrator to the crimes placed too high a burden on a criminal defendant who is without the vast investigatory resources of the State. Rather, in our most recent decision on this issue, we stated:
A criminal defendant is entitled to present evidence in support of the contention that another is responsible for the crime with which he was charged. State v. Harnish, 560 A.2d 5, 9 (Me. 1989); State v. LeClair, 425 A.2d 182, 187 (Me.1981); see M.R.Evid. 401. The evidence "must be admitted if it is of sufficient probative value to raise a reasonable doubt as to the defendant's culpability." State v. Conlogue, 474 A.2d 167, 172 (Me.1984); see M.R.Evid. 402. We have, however, upheld the exclusion of evidence that is "too speculative or conjectural or too disconnected from the facts" of a defendant's prosecution.
* * * * * *
For alternative perpetrator evidence to have "sufficient probative value to raise a reasonable doubt as to the defendant's culpability," Conlogue, 474 A.2d at 172, it must be more than speculative and conjectural. The evidence incriminating another person "must be competent and confined to substantive facts which create more than a mere suspicion that the other person committed the [crime]...." Fortson v. State, 269 Ind. 161, 379 N.E.2d 147, 153 (1978). The connection between the alternative perpetrator and the crime must be reasonably established by the admissible evidence the defendant is prepared to offer. Without such evidence, a defendant cannot be allowed to use his trial to conduct an investigation that he hopes will convert what amounts to speculation into a connection between the other person and the crime. See State v. Williams, 462 A.2d 491, 492 (Me.1983); State v. White, 460 A.2d 1017, 1025 (Me.1983).
Dechaine, 572 A.2d at 134 (footnotes and citations omitted) (emphasis added).
In this particular case, however, the admissible evidence that Robinson was prepared to offer did not reasonably establish a connection between Stillings and the murders. Assuming that Newbert could have testified as to Stillings purported hearsay statements, that evidence amounts to a threat by Stillings on the life of Maguire. Robinson proffered no admissible evidence that would have placed Stillings in the Bangor area, let alone near Maguire's trailer, at the time in issue. Without such evidence, we cannot say that it was an abuse of discretion for the trial court to conclude that Robinson's proffered evidence, at best, established a speculative connection between Stillings and the offenses with which Robinson was charged.

III

Sufficiency of the Evidence
Robinson finally contends that the State's evidence was insufficient to permit the jury to rationally conclude that he committed the charged offenses at around 12:00 a.m. on June 4, 1988. We disagree.
At trial, the State produced a large body of circumstantial evidence that, when viewed in the light most favorable to the State, would allow a jury rationally to find the essential elements of the crime beyond a reasonable doubt. See State v. Barry, 495 A.2d 825, 826 (Me.1985). In summary, the evidence would have allowed the jury to conclude that Robinson had been involved in a romantic relationship with Maguire during 1987 and 1988 and had been intimate with her as recently as May 29, 1988, approximately a week before the murders. Robinson had been present on one occasion when Maguire had flirted with Blanchard during a visit at the home of Maguire's daughter and Blanchard's son-in-law. Robinson admitted intentionally following Maguire and her daughter, in April of 1988, as they went from bar to bar, to a pizza restaurant and finally to Maguire's trailer.
On the evening of June 3, as Maguire visited two bars in Bangor, Robinson appeared at the bars and was seen conversing with Maguire in an "ugly tone of voice," and later, when she returned with Blanchard, *668 Robinson was seen staring at the two of them. According to Robinson, Maguire told him to wait for her at one of the bars but never arrived. Robinson proceeded to look for Maguire in several bars.
While there was some evidence that Maguire and Blanchard were seen by witnesses, alive and well, on Saturday, June 4, a time when the State contended they were already dead, the State produced substantial evidence that the killings took place at about 12:00 a.m. on June 4. Specifically, seven trailer park residents recalled hearing unusual sounds, including what some described as "gunshots" or "bangs," at around midnight. One of the residents recalled seeing, at around the same time, a pickup truck resembling Robinson's pull up in front of Maguire's trailer and a man fitting Robinson's general appearance get out of the truck.
Contrary to his normal practice, Blanchard did not call his mother when he did not come home Friday night. Nor did he appear at his friend's home Saturday morning for a planned fishing trip. Maguire did not attend the wedding and reception of her niece at 1:00 p.m. on Saturday, despite having discussed her plan to attend. Trailer park residents saw no activity in or near the Maguire trailer on Saturday. One resident noted that the curtains in the trailer remained closed during the day and observed a hole, later determined to be a bullet hole, in the trailer. Maguire's daughter was unable to contact her by telephone on Saturday.
Moreover, the activities of the perpetrator, cutting a clothes line, an electrical wire and a cable television wire, apparently in a failed effort to cut the telephone line, and then entering the trailer unnoticed and shooting the victims with multiple shots from a high-powered handgun, strongly indicated that the events occurred during the nighttime rather than the following day. According to the medical examiner, the victims were dead no later than early afternoon of Saturday, June 4 and, more likely, Friday night. The presence of opened and nearly full bottles of beer in the trailer, the fact that Blanchard was wearing a jacket, and the elevated blood-alcohol levels of the victims were indicative that the time of the alleged offenses closely followed the victims' visits to the bars on Friday night.
Robinson, who had not complained to his employer about his wages or working conditions, left Bangor at about 2:00 a.m. on Saturday, June 4, 1988, without any notice, after securing the maximum amount of cash permitted from an automatic teller machine; obtained a larger amount of money from his bank account at an Augusta branch bank when it opened Saturday morning; and then left the State.
Robinson had owned a .44 caliber Llama revolver, one of the three types of guns which could have been used to commit the murders, and he also possessed Norma ammunition that appeared to be of the precise type used in the killings. Although he claimed his firearm was stolen from his truck, he never reported this to the police. He also possessed pliers which, from their configuration, as well as the presence of residue, were consistent with having been used to cut the clothesline and wires at the trailer.
Based on this evidence, and the rational inferences that it supports, we conclude that the State met its burden of producing evidence sufficient to permit the jury to rationally conclude beyond a reasonable doubt that Robinson was guilty of the offenses charged.
The entry is:
Judgments affirmed.
All concurring.
NOTES
[1]  See Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).
[2]  Newbert was similarly under indictment.
