A former model filed a lawsuit on Tuesday accusing the hip-hop mogul Sean Combs of forcing her to perform oral sex on him at his New York City recording studio in 2003.

In the complaint, Crystal McKinney says that when she was 22, an unnamed fashion designer invited her to attend a Men’s Fashion Week event at a restaurant in Manhattan, where she met Mr. Combs, who was a well-known record label impresario and host of the MTV reality show “Making the Band.”

Later that night, according to the lawsuit, Mr. Combs invited her to his recording studio, where Ms. McKinney says she was given alcohol and marijuana that she later came to believe was laced. She says Mr. Combs led her to the bathroom, shoved her head down to his crotch and, after she refused, forced her to perform oral sex on him. Soon after, the lawsuit says, she lost consciousness, later awakening in a cab and realizing that she had been sexually assaulted.

Representatives for Mr. Combs did not immediately respond to requests for comment on the lawsuit.

Mr. Combs, 54, has been facing deepening legal troubles since his former girlfriend, Casandra Ventura, known as Cassie, filed a lawsuit against him last year in which she accused him of sexually and physically abusing her for years. The lawsuit was settled in one day, but three more suits followed from women who accused him of rape. In March, two of Mr. Combs’s homes were raided as part of an investigation that officials said is at least in part a human trafficking inquiry.

The producer and businessman, who is known as Puff Daddy and Diddy, has called the allegations against him false and “sickening,” and he has described the plaintiffs as looking for “a quick payday.”

Mr. Combs’s conduct has come under intense scrutiny in recent days after CNN published footage from 2016 in which he is seen striking, kicking and dragging Ms. Ventura, corroborating part of her lawsuit filed last year. On Sunday, he apologized, saying in a video posted to Instagram, “My behavior on that video is inexcusable.”

Ms. McKinney, who filed her lawsuit in Federal District Court in Manhattan, said learning of the other lawsuits against Mr. Combs led her to file her own. Because the allegations are more than two decades old, which is outside the statute of limitations, the lawsuit is bringing the claim under New York City’s Victims of Gender-Motivated Violence Act, which, for a limited period of time, allows accusers to file civil complaints involving claims after the statute of limitations has run out.

A lawyer representing Mr. Combs, Jonathan Davis, argued in a separate assault lawsuit that the gender violence act should not be used to allow such suits to go forward because another state law specifically extending the statute of limitations for sexual assault had expired.