They cited new evidence provided by the original prosecutor in the case who testified in a recent series of secret sessions that he tried to disqualify the original judge in 1977 on grounds of misconduct but was ordered by his superiors not to do so.
The lawyers also accused the current prosecutors of giving false information to Swiss authorities to support Polanski's extradition to the United States when they knew his potential sentence did not fall within Swiss requirements to order his return.
The appeal said prosecutors were well aware that the now-deceased judge intended for Polanski to serve no more than 90 days in prison when the director pleaded guilty to unlawful sex with a 13-year-old girl.
Swiss authorities have said they will extradite Polanski only if they know he will be sentenced to at least six months behind bars.
Los Angeles County district attorney's spokeswoman Sandi Gibbons said prosecutors were studying the appeal.
"We will respond in writing, which we believe is appropriate," Gibbons said.
The appeal was filed in the California 2nd District Court of Appeal, which has ruled on the case once. Polanski's lawyers accused the current judge in the case, Los Angeles County Superior Court Judge Peter Espinoza, of failing to follow recommendations in the appellate ruling last December.
Espinoza and the district attorney's office ignored the appellate court's urging to "to bring this matter to a prompt and just conclusion," they said. "Indeed, the opposite is true."
While the appeals court blasted apparent misconduct in the case, it refused to order a dismissal and sent it back to Espinoza for further action. Espinoza ruled in January that he could not consider Polanski's request for dismissal or sentencing in absentia without the director appearing in his court.
In Thursday's emergency petition, Polanski attorneys Chad Hummel and Bart Dalton cited the subsequent closed-door testimony by former Deputy District Attorney Roger Gunson, the 1970s case prosecutor.
"Far more serious misconduct, which has been hidden by the prosecution in this case for years, occurred at the highest levels of the district attorney's office in August 1977," the emergency appeal said.
According to the appeal, Gunson testified that in 1977 he tried to challenge now-deceased Superior Court Judge Lawrence Rittenband but his supervisors prevented him from filing it after they consulted with the judge.
"Two of the most senior supervising deputies in the office at that time had secret ... communications with Judge Rittenband about his misconduct in this case, which Rittenband confirmed to them, and they failed to inform the defense or seek Rittenband's disqualification," the appeal said.
The misconduct it referred to was Rittenband's alleged intention to use a 90-day "diagnostic study" in state prison as a complete sentence for Polanski although that section of the penal code was not intended to be used for sentencing.
Gunson was questioned for three days in a "conditional examination" ordered by Espinoza. Such examinations are used to preserve testimony when it appears that a witness will not be available for future proceedings. It usually involves a witness who is ill or is planning to be out of state.
The district attorney's office declined to comment on why such testimony was required. Espinoza had expressed urgency in getting the examination done during a previous hearing.
Polanski's legal team said it based its account of Gunson's comments on their notes taken during the hearing in which they cross-examined him. They asked the appeals court to order unsealing of the transcripts.
Polanski was initially indicted on six felony counts, including rape by use of drugs, child molesting and sodomy. He later pleaded guilty to one count of unlawful sexual intercourse.
Polanski's attorneys say Rittenband sentenced the director in 1978 to the diagnostic study at a prison where he served 42 days. They contend Rittenband told attorneys that would be Polanski's full sentence but he later indicated he was going to renege and order a harsher sentence. Polanski fled before that hearing.
The new appeal focuses on an earlier stage of the case. It said Gunson recalled he was so concerned about Rittenband's inability to be fair to the prosecution that he drafted an application to disqualify the judge and intended to file it before Polanski entered his plea.
Gunson said he detailed contacts between Rittenband and third parties outside the case, including a defense attorney who wanted to be appointed as Polanski's counsel, according to the appeal. He testified that he presented the draft affidavit to Chief Deputy District Attorney Stephen Trott and supervising Deputy Michael Montagna, the appeal said.
Trott is now a senior judge on the 9th U.S. Circuit Court of Appeals.
Gunson said they asked how they could confirm his allegations, and he told them to contact the judge. One or both of them met with Rittenband secretly without telling the defense, the appeal said.
After Polanski was released from prison, Gunson said Rittenband told attorneys he would agree to let Polanski serve the remaining 48 days of the original sentence if he agreed to self-deport himself from U.S.
Gunson said he understood that Polanski could no longer trust the judge, the appeal said.
Montagna, who is retired, told The Associated Press on Thursday that he had no recollection of talking to Gunson about challenging Rittenband and "I never talked to Rittenband about this case, ever." He said he assigned Gunson to the case and then had little involvement and that he did not know what conversations may have taken place between Gunson and Trott.
He described Gunson as a good lawyer, "honest and upright."
Polanski's lawyers alleged that the current district attorney's office has known about the misconduct since 2002. They cited a memo from Deputy District Attorney Richard Doyle, then handling the case, who wrote that Gunson had submitted a 20-page affidavit.
The lawyers said the notes were revealed only in connection with Gunson's testimony and showed there was misconduct before Polanski entered his plea even though prosecutors argued the opposite to the appeals court.
The appeal noted that in its December ruling, the appellate court said all malfeasance occurred post-plea.
Gunson's affidavit now can't be found, the appeal said.
A request for comment was not immediately returned Thursday at Trott's chambers in Boise, Idaho.