The New York Police Department is investigating a second sexual assault complaint against the celebrity chef Mario Batali, a person familiar with the matter said Monday.

In that complaint, which has not been previously reported, a woman told the police on March 15 that Mr. Batali drugged and sexually assaulted her in January 2004 at his Greenwich Village restaurant Babbo. The woman told the police she had been drinking at the bar and went upstairs to use the bathroom, according to the person familiar with the complaint, who spoke on the condition of anonymity. Her next memory was waking up as Mr. Batali was raping her.

On Sunday, “60 Minutes” interviewed a different, unidentified woman who said Mr. Batali had sexually assaulted her in 2005 at the Spotted Pig, a popular restaurant in Greenwich Village owned by the restaurateur Ken Friedman and the chef April Bloomfield. The woman said she had passed out after drinking with him, and woken up with scratches on her leg and semen on her skirt; she called a rape crisis hotline and had a rape kit taken at a hospital. The woman said she reported the incident to the police but did not file a complaint.

J. Peter Donald, assistant commissioner for the Police Department, confirmed Monday that it is now investigating the Spotted Pig incident, but would not confirm the 2004 complaint about Babbo. Danny Frost, a spokesman for the Manhattan district attorney, Cyrus R. Vance Jr., said he could not comment on whether Mr. Vance’s office was investigating Mr. Batali.