The Supreme Court has declined to take a new look at Washington state's top-two primary system amid complaints from political parties that it interferes with their rights.

The justices said they will not hear appeals from the state Democratic and Libertarian parties opposing a system that allows primary candidates to identify themselves as members of a party even when the party objects. The parties said the system could confuse voters.

But the San Francisco-based 9th U.S. Circuit Court of Appeals said there is no evidence of confusion and upheld the system. Under the top-two system, the top two finishers in a primary advance to the general election, even if they're both Democrats or both Republicans.

The Supreme Court upheld the system in 2008 but acknowledged there could be additional challenges.