A Manhattan jury will be asked a narrow question this week: How much money must former President Donald J. Trump pay the writer E. Jean Carroll for defaming her after she accused him of raping her?

Ms. Carroll’s chance encounter decades ago at the Bergdorf Goodman department store, in which she said Mr. Trump shoved her against a dressing room wall, pulled down her tights and forced himself on her, was already the focus of a trial last year. A jury in May awarded Ms. Carroll just over $2 million for the assault and nearly $3 million for defamation over Mr. Trump’s remark in October 2022 calling her claim “a complete con job.”

The trial starting Tuesday focuses on separate statements by Mr. Trump in June 2019, directly after Ms. Carroll disclosed her allegation in New York magazine. At the time, Mr. Trump called her claim “totally false,” saying that he had never met Ms. Carroll, a former Elle magazine advice columnist, and that she invented a story to sell a book.

Now, Mr. Trump says he wants to attend and testify at Ms. Carroll’s trial, something he didn’t do in the earlier case. That’s sparked a bitter dispute between lawyers for Ms. Carroll, 80, and Mr. Trump, 77, over what the former president could say if he took the stand, and whether he would stray beyond strict boundaries the judge has set.

The judge, Lewis A. Kaplan, has ruled that given the jury’s findings in the first trial, Mr. Trump cannot now contest Ms. Carroll’s version of events — as he frequently does in public statements.

“Mr. Trump is precluded from offering any testimony, evidence or argument suggesting or implying that he did not sexually assault Ms. Carroll, that she fabricated her account of the assault or that she had any motive to do so,” Judge Kaplan wrote in an opinion on Jan. 9.