Manhattan prosecutors have decided not to file rape charges against a son of Police Commissioner Raymond W. Kelly after a two-week investigation of a woman’s accusation that he had attacked her late last year inside the Lower Manhattan law office where she worked, prosecutors said in a letter on Tuesday.

The office of the Manhattan district attorney, Cyrus R. Vance Jr., concluded its inquiry into the accusation leveled against Mr. Kelly’s son Greg Kelly, a local television anchor, concluding that “the facts established during our investigation do not fit the definition of sexual assault crimes,” according to a brief letter to Mr. Kelly’s lawyer, Andrew M. Lankler. “Therefore, no criminal charges are appropriate.”

A spokeswoman for the district attorney’s office said it had conducted a “thorough investigation,” interviewing witnesses and analyzing evidence including security logs, text messages, receipts and phone records.

The letter, from the chief of the district attorney’s Sex Crimes Unit, Martha Bashford, the assistant district attorney assigned to handle the case, said the witnesses included the accuser and Mr. Kelly, “both of whom were cooperative and were interviewed in the first days of the investigation.”