There are certainly calls that do not merit a crime report: a victim’s account of an alleged crime can be deemed dubious, for example.

However, some commanders said, officers sometimes bend to pressure by supervisors to eschew report-taking. “Cops don’t want a bad reputation, and stigma,” one commander said. “They know they have to please the sergeants.” Like several other officers and supervisors, he spoke only on the condition of anonymity for fear of retribution.

The sergeants, in turn, are acting on the wishes of higher-ups to keep crime statistics down, a desire that is usually communicated stealthily, the commander said. As an era of low crime continues, and as 2011 draws to a close with felony numbers running virtually even with last year’s figures, any new felony is a significant event in a precinct and a source of consternation to commanders.

On the Upper West Side in July, a man in red shorts climbed through a window into the living room where Katherine Davis, 65, was reading the paper. She ran, a few steps ahead of him, and locked herself in an adjacent apartment, where she watched through the peephole as the man searched for her before he left.

Officers drove her around to look for the intruder, unsuccessfully. Ms. Davis asked if they could take fingerprints. But the officers said, “Oh, no, that’s only if you have a detective, or investigation,” she recalled. She asked for a case number.

“They said, ‘There is no case number,’ ” she said.

No one came to interview her or to seek videotape from the numerous surveillance cameras nearby, she said. That is where things ended.