The Supreme Court on Monday let stand the murder conviction of Kennedy cousin Michael Skakel, who is serving a prison term of at least 20 years.

The justices declined to take Skakel's appeal of his conviction in the beating death of his Greenwich, Conn., neighbor, Martha Moxley, 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.

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 state legislature removed the five-year deadline in such cases.

Click here to read the case materials on Skakel (pdf)

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.