Critics have questioned the extent to which CompStat could be undermined by departmental incentives to keep crime low, as reflected in statistics. Patrick J. Lynch, president of the Patrolmen’s Benevolent Association, raised that specter again on Friday while saying the union would “vigorously defend” the accused officers.

“It’s an artificial way of keeping felonies down with fewer officers on the street, a problem that we still experience today,” he said.

In one high-profile 2010 episode involving allegations of data being doctored, a police commander, Deputy Inspector Steven Mauriello, and four officers faced internal charges based on another officer’s claims that crime complaints in the 81st Precinct in Brooklyn had been manipulated. Inspector Mauriello specifically was charged with failing to record a grand larceny complaint and with impeding the department’s investigation, officials said at the time.

The current inquiry into the 40th Precinct crime data grew out of an anonymous tip to the Internal Affairs Bureau about a “mischaracterization of crime reporting going on,” Lawrence Byrne, the deputy commissioner of legal matters, said.

In conducting the audit, the department’s Quality Assurance Division reviewed 1,558 crime complaint reports filed from May to August 2014 — the first four months of Inspector Johnson’s tenure — and examined 911 calls and so-called radio runs during that time to assess officers’ responses, the police said.

Forty-four complaints prompted immediate concern, including six in which the narrative in police reports did not match the crime alleged. In fewer than 10 cases, officers simply did not record a complaint that was made. Most of the improperly classified complaints involved five low-level offenses — petit larceny, lost property, misdemeanor assault, criminal mischief and criminal trespass — that should have been recorded as more serious crimes.

The police said they did not believe any of the reports at issue led to an arrest.

Mr. Davis said the auditors believed they had captured the extent of the wrongdoing. “They think they wrapped it up for the audit period,” he said, adding, “It’s disturbing, the scope of this.”