LOS ANGELES — Alan M. Dershowitz, a lawyer whose celebrity clients have included the heiress Patty Hearst and the hacker Julian Assange, is seeking to lead what could be the final effort to end the legal case against the film director Roman Polanski, who fled the United States before final sentencing on a statutory rape charge in 1978.

In connection with a Los Angeles County Superior Court filing on Monday, Mr. Dershowitz, who is based in Massachusetts, is asking permission to represent Mr. Polanski in California.

The filing charged prosecutors with providing false information to support a recent attempt to have Mr. Polanski extradited from Poland. It also demanded a hearing aimed at closing his case, based partly on fresh testimony that a Superior Court judge, in 2009, had unethically prejudged issues related to Mr. Polanski’s prosecution, and had a secret plan to jail him at least briefly, even while limiting his actual sentence to time served.

The filing is likely to draw new attention to a legal process that has risen and fallen in the public consciousness for almost four decades. It also caps a year in which seemingly dormant claims of sexual assault against Woody Allen and Bill Cosby found new life. Unlike Mr. Polanski, neither Mr. Allen nor Mr. Cosby was charged with crimes; however, they have been publicly excoriated for, and have strongly challenged, claims of illicit sexual behavior.