The case involved the Beastie Boys' sampling six seconds of Jazz flutist James Newton's 1978 song, "Choir."
The sample was used on "Pass The Mic" off the New York group's 1992 LP, Check Your Head, the hip-hop web site SOHH.com reported.
A three-judge-panel last year ruled the group obeyed copyright laws by paying a license fee for sampling Newton and didn't have to pay to license the foundational composition.
The verdict supported a lower-court dismissal in favor of the group and the 9th Circuit decided not to reconsider its decision.
"We hold that Beastie Boys' use of a brief segment of that composition, consisting of three notes separated by a half-step over a background C note, is not sufficient to sustain a claim for infringement of Newton's copyright," Chief Judge Mary Schroeder wrote in her statement.