The appeal began last summer when Polanski's lawyers pressed to dismiss the case in California that has haunted the 76-year-old director since he fled to France three decades ago.
Polanski himself is confined to house arrest in his Swiss chalet in the resort town of Gstaad, and his freedom is in the hands of judges in two countries.
Any decision by a three-judge panel of the California 2nd District Court of Appeal will not immediately affect Polanski's current predicament of fighting extradition from Switzerland to the United States. Still a victory in California would put the issue before a judge who already found "substantial misconduct" in the case.
Los Angeles Superior Court Judge Peter Espinoza made the finding after watching an HBO documentary on the case, but he declined to act because of a well-established doctrine that says fugitives are not entitled to a court hearing if they don't show up.
Polanski has been a wanted man since he fled to France on the eve of sentencing in 1978 for having unlawful sexual intercourse with a 13-year-old girl.
He was accused of plying the teen with champagne and part of a Quaalude pill and then raping her during a modeling shoot at Jack Nicholson's house in 1977. He was initially indicted on six felony counts, including rape by use of drugs, child molesting and sodomy. He pleaded guilty to one count of unlawful sexual intercourse.
He sought dismissal of the case in July after the HBO documentary uncovered new details about alleged back room dealings between the judge and a prosecutor who said he meddled in the case. The judge is deceased and the former prosecutor recanted his statements after Polanski's arrest.
Lawyers in the case refused to comment, but the defense argued in court papers that Polanski's constitutional rights were clearly violated.
"There is no reported case like it," wrote defense attorney Chad Hummel. "It has lasted 30 years and has been infected from the outset by extraordinary misconduct."
The appeal was filed in July when Polanski was a free man - two months before being arrested in Switzerland and jailed as a fugitive.
He was released last week under house arrest conditions and is living at his chalet in Gstaad. He is under electronic monitoring while his attorneys seek to block his extradition to the United States.
Prosecutors claim Polanski's arrest - on his way to collect an award at a film festival - has made the appeal unnecessary because he can be returned to California and can argue for the dismissal in person. They unsuccessfully asked the court to reject the appeal.
Legal experts said they'd be surprised if Polanski prevails in the appellate court.
In exile, Polanski's career has continued to flourish. He received a directing Oscar in absentia for the 2002 movie "The Pianist." While still in the United States, he directed such classic films as "Chinatown" and "Rosemary's Baby." He was working on a new movie when he was arrested.
Unlike his arrest 32 years ago, the current case has ignited public passions on both sides. A number of movie stars and French officials lined up with the director at the outset but some withdrew their support following public outrage when details of the crime were published.
Polanski's victim, Samantha Geimer, has repeatedly asked for dismissal of the charges against Polanski. Her attorney filed a declaration in the appeals case last summer stating that the case's re-emergence has caused her health and work problems.
She sued Polanski years after he fled and the director agreed to pay a $500,000 settlement. It is unclear how much of the money she received.