Polanski, 76, was arrested Sept. 26 in Zurich in connection with the decades-old Los Angeles crime and imprisoned until last week when he was granted bail and placed under house arrest in his Swiss chalet.
The internationally famous filmmaker, who had been living in France but was in Switzerland to attend a film festival at the time of his arrest, has not traveled to the United States since he pleaded guilty in a Los Angeles court to having unlawful sex with a minor and then fled the country before he could be sentenced. He was accused of drugging and raping a 13-year-old girl.
Polanski's lawyers have alleged misconduct on the part of the Los Angeles criminal justice system at the time of the plea deal, and are fighting extradition from Switzerland to the United States.
The Los Angeles Times quoted Polanski's attorney, Chad S. Hummel, as telling the panel of three appellate court justices Thursday the case should be thrown out due to an "astonishing record of misconduct" by the district attorney's office and Judge Laurence J. Rittenband, who originally heard the case.
The Times said the appeals court is expected to decide whether a trial judge can consider Polanski's petition to dismiss the case and review evidence of misconduct without the director first coming back to California, which he has adamantly refused to do.
An attorney representing the victim also spoke at Thursday's hearing and encouraged the panel to dismiss the case, the newspaper said.
Notable deaths of 2014 [PHOTOS]