In New York housing projects, police officers can demand identification from people who are hanging out in a public space, like a building lobby. Even if they prove that they live in the building, officers may cite them for “lingering.”

It is not a crime, but it is a violation of the New York City Housing Authority’s rules.

There are many such rules that govern life in the projects, like no playing in the hallways and no barbecuing without a permit. Breaking any of them can put a tenant at risk of eviction from a system that offers some of the city’s most affordable housing.

Simply waiting outside for a pizza delivery can draw the attention of the police, said Ronald Thomas, 24, who described being approached by two officers recently in the Red Hook Houses in Brooklyn. Only the deliveryman’s arrival spared Mr. Thomas a citation, he said.

Amid broader calls to ratchet down the pressure on low-level crimes, little scrutiny has been paid to a routine patrol tactic used by the Police Department: In public housing, officers walking a beat are watching not only for offenses big and small but also for behavior that is not illegal at all.