FILE - In this Feb. 24, 2016, file photo, Michael Skakel leaves the state Supreme Court after his hearing in Hartford, Conn. The Supreme Court is leaving in place a decision that vacated a murder conviction against Kennedy cousin Michael Skakel. The high court on Monday declined a request from the state of Connecticut to hear the case. (AP Photo/Jessica Hill, File)

FILE - In this Feb. 24, 2016, file photo, Michael Skakel leaves the state Supreme Court after his hearing in Hartford, Conn. The Supreme Court is leaving in place a decision that vacated a murder conviction against Kennedy cousin Michael Skakel. The high court on Monday declined a request from the state of Connecticut to hear the case. (AP Photo/Jessica Hill, File)

WASHINGTON (AP) — The Supreme Court announced Monday that it is leaving in place a decision that vacated a murder conviction against Kennedy cousin Michael Skakel.

Skakel was convicted in 2002 of the 1975 bludgeoning death of Martha Moxley, who lived across the street from the Skakel family in Greenwich, Connecticut, and whose body was found in her family’s backyard. Both Skakel and Moxley were 15 at the time of her death.

The high court’s refusal to hear the case means that a 2018 decision by Connecticut’s highest court throwing out Skakel’s conviction will stand. Connecticut’s highest court based its decision on Skakel’s attorney’s failure to seek out an additional alibi witness.

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Though it would be difficult, the state could retry Skakel, who is a nephew of Robert F. Kennedy’s widow, Ethel Kennedy. The state has not said how it would proceed if the Supreme Court declined to intervene. Top Connecticut prosecutors said Monday they appreciated the Supreme Court’s consideration of their request to hear the case, but declined further comment.

Moxley’s mother said Monday she was disappointed with the Supreme Court’s decision. Dorthy Moxley, 86, who now lives in New Jersey, said she has no doubt that Skakel killed her daughter and she wants to see him back in prison, but will support whatever decision Connecticut prosecutors make about whether to retry him.

“The state of Connecticut had a very, very, very good case, and we absolutely know who killed Martha,” she said. “If Michael Skakel came from a poor family, this would have been over. But because he comes from a family of means they’ve stretched this out all these years.”

Skakel’s appellate lawyer, Roman Martinez, said he hoped Connecticut prosecutors would decide against retrying Skakel.

“Over the past 10 years, two Connecticut courts — including the Connecticut Supreme Court — have painstakingly reviewed every detail of Michael Skakel’s case,” Martinez said. “Both reached the same conclusion: Michael’s conviction violated the U.S. Constitution.”

Skakel’s case has spent nearly two decades winding its way through the court system after he was charged in 2000 with Moxley’s killing. After a jury convicted Skakel, he argued that his lead trial lawyer did an inadequate job representing him, including by failing to contact an additional witness who could confirm his alibi for the time of the killing.

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Skakel says he was watching an episode of the “Monty Python” television show at his cousin’s house at the time Moxley was killed. Moxley was beaten with a golf club that belonged to Skakel’s mother.

Prosecutors told the Supreme Court that if Skakel “had been provided the assistance of an attorney who undertook only half the efforts his defense team undertook in this case, he still would have been afforded far better representation than that provided for the typical criminal defendant.”

Skakel served more than 11 years in prison before being freed on $1.2 million bail in 2013 when a judge overturned his conviction, citing errors by his lead trial lawyer Michael Sherman, who has defended his work.

But Connecticut’s Supreme Court reinstated Skakel’s conviction in December 2016, ruling 4-3 that Skakel was adequately represented. That decision didn’t last.

The Connecticut Supreme Court justice who wrote the majority opinion, Peter Zarella, retired immediately after the decision was announced, and Skakel asked that the decision be reconsidered. A new justice, Gregory D’Auria, sided with the three justices who had previously dissented and in May reversed the court’s original decision. It is that ruling that the Supreme Court left in place, turning away the case without comment, its usual practice when it declines to hear a case.

D’Auria and his colleagues’ ruling was based on Sherman’s failure to seek out the additional witness who could confirm Skakel’s alibi.

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Associated Press reporter Dave Collins reported from Hartford, Connecticut.