The New York City Ballet wants to swan-dive out of a lawsuit filed by a former dancer who claims her ex-boyfriend recorded and snapped photos of their sexual encounters to show to other members and even donors.

The famed dance company filed papers in Manhattan Supreme Court on Thursday saying it should not be held accountable in the case.

The “plaintiff never claims to have been employed by the Ballet because she was not,’’ the document says.

Ex-ballet dancer Alexandra Waterbury has called the company a “breeding ground for sexual exploitation” while suing over former boyfriend dancer Chase Finlay’s behavior.

Waterbury criticized the ballet for welcoming a dancer back from rehab, saying it sent a message to Finlay and others “that it was acceptable . . . to abuse substances and degrade, demean, dehumanize and physically abuse women.”

She also has accused a donor of suggesting that the “girls’’ be tied up so the men could “abuse them like farm animals.’’

The New York City Ballet attacked the former ballerina in the documents, stating it had no reason to “safeguard” her just because she was in a relationship with a ballet employee.