(CNN) -- The United States has formally asked Switzerland to extradite film director Roman Polanski, Swiss authorities said Friday.

Director Roman Polanski fled the U.S. more than 30 years ago and was detained in Switzerland in September.

The Academy Award-winning director was arrested in Switzerland last month on a U.S. arrest warrant stemming from a 1977 sex case involving a 13-year-old girl. He is fighting extradition.

The U.S. Embassy in Berne submitted the formal extradition request to Switzerland's Federal Office of Justice on Thursday night, Swiss justice officials said.

Swiss justice officials said they will now forward the extradition request to the Canton of Zurich, where Polanski is being held, so an extradition hearing can be held.

If a decision is made for Polanski to be extradited, the director may appeal to the Federal Criminal Court, justice officials said.

Earlier this week, a Swiss court refused a request to release Polanski on bail pending an extradition battle, saying that he posed a high flight risk. He was given 10 days to appeal the decision.

The Academy Award-winning director was arrested in Switzerland last month on a U.S. arrest warrant stemming from a 1977 sex case.

Polanski pleaded guilty in August 1977 to having unlawful sex with a 13-year-old girl five months earlier. He was 43 at the time, and is now 76.

Los Angeles, California, prosecutors dropped other charges in exchange for his guilty plea.

But Polanski fled the country before he was sentenced, after he learned the judge might not go along with the short jail term he expected to get from the plea agreement.

Polanski remained free -- mostly living in France -- before he was arrested in Switzerland on a 31-year-old arrest warrant. Los Angeles authorities said they sought his arrest when they learned he would be traveling to Switzerland for a film festival last month.

Polanski agreed to pay his sexual assault victim $500,000 to settle a damage claim she filed against him nearly 12 years after the crime, according to court papers released October 2.

Polanski still owed the money -- plus another $100,000 interest -- three years after the 1993 settlement, according to the documents.

The victim sought money for damages suffered when Polanski had sex with her. She claimed Polanski plied her with alcohol and quaaludes during a photo shoot at the Hollywood Hills home of actor Jack Nicholson.

It's not clear if Polanski ever completed paying the debt to the woman, although the court papers document efforts by her lawyers to garnish residuals and other payments owed to Polanski by the Screen Actors Guild, movie studios and other Hollywood businesses.

The victim came forward long ago and made her identity public -- saying she was disturbed by how the criminal case had been handled. Samantha Geimer, now 45, a married mother of three, called in January for the case to be tossed out.

Polanski's arrest has divided public opinion, even in Hollywood. Some high-profile filmmakers, such as Woody Allen, Martin Scorsese and Pedro Almodovar, have called for his release. Others, including actors Kirstie Alley and Paul Petersen, refuse to defend him.

Polanski won an Academy Award for Best Director in 2003 for "The Pianist." He was nominated for a best director Oscar for "Tess" and "Chinatown," and for best writing for "Rosemary's Baby," which he also directed.

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