Prosecutors who say Bill Cosby belongs in prison are asking the United States Supreme Court to throw out an appellate court ruling earlier this year that overturned his 2018 conviction for sexual assault on due process grounds.

Mr. Cosby walked free from prison in June after serving less than three years of a three-to-10-year sentence.

His release followed a ruling by the Pennsylvania Supreme Court that Mr. Cosby’s rights had been violated when the Montgomery County District Attorney’s office pursued a criminal case against him despite what the appellate court found was a binding “non-prosecution agreement” given to him by a previous district attorney.

It was a dramatic reversal in one of the first high-profile criminal convictions of the #MeToo era.

The petition for review, filed last Wednesday by the district attorney’s office but only made public Monday, challenges that decision, arguing that the Pennsylvania Supreme Court erred in its ruling.

The Pennsylvania high court’s decision came in the case of Andrea Constand, a former Temple University employee to whom Mr. Cosby had become a mentor. He was arrested in 2015 on charges that he had drugged and sexually assaulted her at his home in a Philadelphia suburb 11 years earlier.

The arrest came at a time when dozens of other women had already come forward to accuse Mr. Cosby of sexual assault or misconduct.

A spokesman for Mr. Cosby, Andrew Wyatt, released a statement that referred to the decision to seek Supreme Court review as “a pathetic last-ditch effort.”

“In short, the Montgomery County D.A. asks the United States Supreme Court to throw the Constitution out the window, as it did, to satisfy the #metoo mob,” the statement said. “There is no merit to the DA’s request which centers on the unique facts of the Cosby case and has no impact on important federal questions of law.”

The accusations against Mr. Cosby, and his eventual conviction on three charges of aggravated indecent assault, painted a disturbing portrait of a man who for decades had brightened America’s living rooms as a beloved entertainer and father figure.

Mr. Cosby has consistently denied the accusations that he was a sexual predator, suggesting that the encounter with Ms. Constand, and those with other accusers, had been completely consensual.

It is by no means certain that the U.S. Supreme Court will agree to hear the case. The court denies the vast majority of petitions seeking review.

The justices only consider cases that involve federal law, and they rarely hear cases merely to correct erroneous rulings. Instead, they generally agree to hear cases in which lower courts have reached differing conclusions or ones involving legal issues of great public importance.

Some legal experts had not expected prosecutors to file an appeal to the Supreme Court, seeing the case as a matter of state rather than federal law, and one that involves a specific set of circumstances that do not involve far-reaching constitutional issues.

For the appeal to succeed, the justices would have to decide that the Pennsylvania Supreme Court’s decision relied on and misinterpreted a federal law or constitutional provision, experts said.

“The district attorney’s office really strains in its petition to make this into a precedent-setting issue — it’s not,” said Shan Wu, a former federal prosecutor in Washington, D.C., who has followed the case. “The unique facts make it highly unlikely that it would ever arise again.”

Mr. Cosby’s lawyers have 30 days to respond, though they may seek an extension.

Mr. Cosby’s appeal to Pennsylvania’s highest court had argued, among other issues, that the entertainer had relied on a previous prosecutor’s statement in 2005 that Mr. Cosby would not face charges in the case.

The district attorney at the time, Bruce L. Castor Jr., had said he made the non-prosecution agreement verbally to Mr. Cosby’s lawyer, after determining there was insufficient evidence to win a prosecution on sex assault charges. He has pointed to a news release he issued announcing the end of the criminal investigation as evidence that an immunity agreement existed. He has subsequently testified that the agreement was intended to compel Mr. Cosby to testify in any civil suit that Ms. Constand might file by removing Mr. Cosby’s ability to exercise his Fifth Amendment right against self-incrimination.

Shortly after the criminal investigation was dropped, Ms. Constand did sue Mr. Cosby, and settled in 2006 for $3.38 million.

During testimony in the civil suit, Mr. Cosby acknowledged giving quaaludes to women he was pursuing for sex — evidence that played a key part in the criminal prosecution later brought by Mr. Castor’s successors.

As the criminal case proceeded, the trial court — and an intermediate appeals court — found that no formal non-prosecution agreement ever existed.

But in its 6-1 ruling, the Pennsylvania Supreme Court found that Mr. Cosby had, in fact, relied on Mr. Castor’s assurances that he wouldn’t be prosecuted and that the subsequent decision by a successor to charge Mr. Cosby violated the entertainer’s due process rights. The court barred a retrial, though two of the judges who voted in the majority dissented on that remedy.

“Petitioning to ask the High Court for review was the right thing to do,” Montgomery County District Attorney Kevin R. Steele said Monday in a statement, “because of the precedent set in this case by the majority opinion of Pennsylvania Supreme Court that prosecutors’ statements in press releases now seemingly create immunity.”

The district attorney’s office referenced an argument put forward by one of the Pennsylvania Supreme Court justices, Kevin Dougherty, who said in an opinion that no district attorney had the “power to impose on their successors — in perpetuity, no less — the kind of non-prosecution agreement that Castor sought to convey to Cosby.”

In their 33-page filing, the prosecutors also tried to counter the argument that Mr. Cosby had a right to rely on what Mr. Castor said was a promise not to prosecute him further, asserting that “a reasonably prudent person would have been reckless to rely on a supposed guarantee that the prosecutor did not clearly convey and may not have had the power to grant.”

Since being freed, Mr. Cosby, 84, has portrayed the decision as a full exoneration. The chief justice of the Pennsylvania high court, Max Baer, has said, though, that the court’s ruling did not find Mr. Cosby innocent, only unfairly prosecuted.