Word from police officials came quickly: The targeted killings of two New York City police officers meant that officers on foot patrols must walk only in pairs, and uniformed sentries would now guard each precinct station house.

They were new orders to a force that was already racking up overtime covering demonstrations. But William J. Bratton, the police commissioner, assured reporters that there would be no letdown in enforcement.

Then the latest official statistics came in.

Arrests for crimes large and small, as well as tickets for minor infractions, are down drastically across the city. The department has not said whether it believes that officers are acting in concert — as a result of a specific job action — or whether the officers’ deaths produced a spontaneous response.

The two precincts most directly affected by the deaths — the 79th, where Officers Rafael Ramos and Wenjian Liu were gunned down as they sat in their patrol car on a Brooklyn street; and the 84th, where they were usually assigned — saw a single criminal summons in the week that ended Sunday, according to Police Department statistics. Officers in those precincts wrote no parking or traffic tickets. By contrast, the combined tally of criminal summonses alone during the same week last year reached 130, the department statistics showed.