WASHINGTON (AP) – Kennedy cousin Michael Skakel lost a longshot effort to win reversal of his murder conviction when the Supreme Court on Monday declined to take his case.

The justices refused, without comment, to review Skakel’s conviction in the beating death of Martha Moxley, his neighbor in Greenwich, Conn., 31 years ago when the two were teenagers. Skakel, a nephew of Ethel Kennedy, was convicted in 2002.

Now 46, Skakel is serving 20 years to life in prison.

“We’re very pleased,” said prosecutor Jonathan Benedict. “This has been researched for years. This is not unexpected.”

Skakel’s lawyer, former Solicitor General Theodore Olson, had argued that the deadline for prosecuting Skakel passed 19 years before he was arrested in January 2000.

At the time of Moxley’s killing, Connecticut had a five-year statute of limitations on murder cases that did not involve the death penalty. One year later, in 1976, the legislature removed the five-year deadline in such cases.

The Connecticut Supreme Court upheld Skakel’s conviction, overturning its earlier holding that the new law did not apply to crimes committed before its enactment. The legislature intended to remove the deadline for prosecution for all crimes, like Moxley’s killing, for which the statute of limitations had not yet expired, the state court said.

Olson said the state court was wrong and that applying the new law to this case violated Skakel’s constitutional rights.

On Monday, Olson reiterated in a statement that “we firmly believe that the Connecticut Supreme Court violated Mr. Skakel’s due process rights.” Because the Supreme Court denied the petition without opinion, “it does not mean the court rejected the merits of Mr. Skakel’s argument,” he said.

Authorities say Skakel beat Moxley to death with a golf club. They also accused Skakel’s wealthy family of a cover-up to thwart his prosecution.

Some of Skakel’s friends and classmates testified that he was romantically interested in Moxley and was jealous because his older brother was competing for her affections.

Skakel’s defense also argued that prosecutors failed to hand over a police sketch that they said resembled an earlier suspect.

Separately, Skakel is seeking a new trial based on a claim by a former schoolmate that two of his friends may have killed Moxley. But the man, Gitano “Tony” Bryant, has since refused to testify at upcoming hearings.

Benedict, the prosecutor, has accused Bryant of making up the account after he exercised his Fifth Amendment right against self-incrimination when he was deposed.

Hope Seeley, Skakel’s attorney for the Bryant matter, said in a statement Monday that Skakel deserves a new trial because Bryant and the two men he implicated have invoked their Fifth Amendment rights. She also said a state investigator had a conflict of interest because he was paid in connection with a book about the case.

“All Mr. Skakel asks is that the new information be examined and considered by a jury so that he may finally receive a fair trial,” Seeley said.

Seeley has said she will file a petition in state court arguing that Skakel had ineffective counsel at his 2002 trial, a claim disputed by Skakel’s trial lawyer.

The case is Skakel v. Connecticut, 06-52.