Ms. Waterbury, who studied from 2013 to 2016 at the academy affiliated with the company, the School of American Ballet, blames the company in her suit for condoning a “fraternity-like atmosphere” that “permeates the Ballet and its dancers and emboldens them to disregard the law and violate the basic rights of women.” As an example, the lawsuit says that the company was aware that Mr. Finlay had caused extensive damage to his hotel room in Washington after hosting a party there earlier this year.

Charles W. Scharf, the chairman of the board at City Ballet, said in a statement that the company had not condoned any of the behavior mentioned and that it “has no liability for the actions specified in the complaint and has taken the appropriate disciplinary actions for the dancers involved.”

Ms. Waterbury’s lawsuit says that she was not alone in being victimized and that nude photos of other female dancers were also shared on the text-chain, often accompanied by lewd and misogynistic language.

The suit says a donor wrote to Mr. Finlay about his desire to “violate” dancers at another company, and added, “I bet we could tie some of them up and abuse them like farm animals.” It said Mr. Finlay replied “or like the sluts they are.”