Stephanie Lazarus was arrested in connection with the 1986 killing of Sherri Rasmussen, her ex-boyfriend's wife. She was shot three times in the chest at her Van Nuys townhouse.
Rasmussen's husband told police that Lazarus had repeatedly threatened her.
Detectives say the 51-year-old art crimes detective is linked through DNA evidence which is a bite mark on the victim's arm.
Prospective jurors filled out questionnaires and were asked if it would be a hardship to serve on the trial, which is expected to last up to six weeks.
Lazarus has pleaded not guilty. Opening statements could begin next week.
The Associated Press contributed to this story.