They fault Andrea Constand's lawyers for the weekend release of the transcript to news outlets including The New York Times and The Associated Press. They asked a judge to enforce undisclosed terms of the confidential agreement that settled the former Temple University employee's sexual-assault lawsuit.
Constand's lawyer, Dolores Troiani, did not immediately return a message Thursday.
A court reporting service she hired to take Cosby's deposition said this week that it thought a recent unsealing order included the deposition. A federal judge had unsealed other motions in the case, but the deposition has never been filed in court.
And this week, new Cosby lawyer Monique Pressley has given television and other news interview defending Cosby and discussing the deposition.
Cosby said in the deposition that he engaged in consensual activities with Constand after giving her three Benadryl pills for stress.
Constand said that she was drugged, rendered semi-conscious and then sexually assaulted.
The depositions are the only time Cosby is known to have responded under oath to claims by more than two dozen women that he drugged them, molested them or made unwanted sexual advances. Two of the women were 19 at the time.
The Constand case had stayed largely out of view from 2006 until last year, when comedian Hannibal Buress called out Cosby's behavior onstage and more accusers came forward.
In their petition Thursday, Cosby's lawyers also criticize Constand for tweets they say violate the agreement, including one last year in which she said, "I won't go away, there is a lot more I will say.
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