The report found that new recruits to the unit were not given enough training and that requests for more staff members had been largely unanswered for the better part of a decade. In part because of these shortcomings, the unit has focused on rapes by people unknown to the victim — “stranger rapes” — while giving less attention to rapes by acquaintances.

In 2011, the report said, one deputy police commissioner responded to concerns about staffing by telling the Special Victims Division it did not have to investigate every misdemeanor sex crime, a direction the unit ignored.

Stories that hinted at issues with the N.Y.P.D’s approach to sexual assault have been trickling out for years. In The Wall Street Journal this week, a woman who had been raped said she couldn’t get a detective to return a phone call, while another said a detective asked her how much she drank on the night of her assault, making her feel as though she were to blame. The stories echoed an earlier report from The New York Times in 2010 in which four women described unsympathetic treatment from Special Victims Division detectives assigned to their cases.

The Police Department budget has grown by roughly $814 million, to $5.6 billion, over the past four years under Mr. de Blasio. But when we asked N.Y.P.D officials for the size of the Special Victims Division budget, they said they didn’t have that information, the same response Mr. Peters said they gave him months ago. “They were not able to provide us with budget breakdowns, which by the way is itself concerning,” Mr. Peters said. “Where you put your resources demonstrates what your priorities are.”

Advocates for sexual assault survivors say Mr. Osgood made substantial improvements to the unit even as his requests for more resources were ignored. Last year, for example, he introduced a training technique, Forensic Experiential Trauma Interview, to help sex crime victims remember key details that could help solve a case.

“I’ve never encountered another special victims investigator who can match Osgood’s expertise or his dedication to these cases,” said Jane Manning, director of advocacy at Women’s Justice NOW. The N.Y.P.D. would not let us talk to Mr. Osgood. Asked why, Mr. Donald said he thought that talking to Mr. Shea was “quite sufficient.”

Mr. Osgood attended an April 9 City Council hearing on the Department of Investigation report with top police officials, but he didn’t testify.