Cindy Lee Garcia, an actress in the anti-Muslim film “Innocence of Muslims” refiled her case in federal court Wednesday after an unsuccessful attempt last week to convince a California state judge to order YouTube to remove the movie. This time, Garcia is adding copyright claims to her suit of unfair business practices, fraud and slander.

She’s also continuing to demand that YouTube, the video-sharing website owned by Google Inc., take down the 14-minute trailer for the film. Her argument, according to the suit, will stipulate...