HARTFORD — Eleven states are asking the U.S. Supreme Court to hear Connecticut's appeal in the murder case of Kennedy cousin Michael Skakel and reinstate his conviction.

The states filed a friend-of-the-court brief on Monday, saying a ruling in Connecticut's favor is needed to thwart excessive appeals that focused on mistakes made by defense lawyers. The court has not yet decided whether to hear Connecticut's appeal.

Skakel, a nephew of Robert F. Kennedy's widow, Ethel Kennedy, cited his trial lawyer's failure to contact an alibi witness in his successful appeal to the Connecticut Supreme Court.

The state court in 2016 upheld Skakel's 2002 murder conviction in the bludgeoning death of Martha Moxley in their wealthy Greenwich neighborhood in 1975, when they were teenagers. But the court reversed that ruling in May and vacated the conviction, after a justice in the 4-3 majority retired and a new justice sided with Skakel — a move that has also drawn scrutiny.

Connecticut prosecutors argue the state high court did not properly weigh the overall performance of Skakel's defense, which they described as vigorous. They say the U.S. Supreme Court needs to correct a misperception by other state and federal courts that any mistake by defense counsel demonstrates incompetence and warrants a new trial.

The friend-of-the-court brief, filed by Utah Attorney General Sean Reyes' office, said allowing the nitpicking of defense lawyer performance produces a variety of problems, including flooding the courts with appeals as a result of lower legal standards and making it harder for defendants to find lawyers willing to undergo such scrutiny.

"The Connecticut Supreme Court's standard would impose impossible costs on the States, which already spend billions of dollars annually on indigent defense," the brief says.

The states joining Utah in the brief include Alaska, Arizona, Indiana, Kansas, Louisiana, Maryland, Nebraska, North Carolina, South Carolina and Texas.

The central issue is the different interpretations by courts of the 1984 U.S. Supreme Court ruling in Strickland v. Washington, which deals with how to assess lawyers' performance.

Skakel's attorney in the U.S. Supreme Court case, Roman Martinez, declined to comment Wednesday. Martinez informed the court this week that he would not be filing a response to Connecticut's request for the court to hear the case.

After 25 years of investigations into the Moxley killings and books about the case being published, Skakel was arrested in 2000, convicted of murder in 2002 and sentenced to 25 years to life in prison. He served 11 years behind bars before being freed on $1.2 million bail in 2013 when a lower court judge overturned his conviction. He has remained free since.

His appellate lawyers argued his trial lawyer, Michael "Mickey" Sherman, failed to contact a witness who could confirm Skakel's alibi that he was miles away watching a "Monty Python" television show when Moxley was beaten to death with a golf club. Sherman defends his representation of Skakel.

State prosecutors say Sherman presented other witnesses for that alibi, and argue Skakel could have killed Moxley when he came home that night. Prosecutors also cited incriminating statements made by Skakel to other people who defense lawyers say were not credible.

Prosecutors have suggested that Skakel became enraged at Moxley because she seemed more interested in his older brother, Thomas, an early suspect in the slaying.