Summer Zervos, a former contestant on “The Apprentice” who accused President Trump of sexual assault, is seeking records to prove that he defamed her by calling her a liar.

A lawyer for Ms. Zervos, who is suing Mr. Trump for defamation in New York, said on Wednesday that subpoenas had been issued both to Metro-Goldwyn-Mayer, which owns archives of the reality show, and to the Beverly Hills Hotel, where Ms. Zervos says he groped her in 2007.

“We’re gathering evidence that we believe will prove that the defendant lied when he falsely denigrated Ms. Zervos and when he denied sexually assaulting her,” said the lawyer, Mariann Wang of Cuti Hecker Wang.

Ms. Zervos, a Republican, was among the more than 10 women who came forward during the 2016 presidential campaign to accuse Mr. Trump of inappropriate sexual contact. He denied all of their claims.