The U.S. 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, without comment, to take Skakel’s appeal of his conviction in the beating death of his neighbor, Martha Moxley, 31 years ago when the two were teenagers. Skakel, a nephew of Ethel Kennedy, the widow of Sen. Robert F. Kennedy, was convicted in 2002.