Law enforcement officers stand, with some turning their backs, as New York City Mayor Bill de Blasio speaks on a monitor outside the funeral for NYPD officer Wenjian Liu in Brooklyn on January 4, 2015. (REUTERS/Shannon Stapleton)

New York police are still apparently protesting on the job. The New York Times reports this week that arrests are dramatically down across the city for the second week, as are parking and traffic tickets and criminal summonses. In the Coney Island precinct last week, police didn't issue a single parking ticket or infraction for "quality of life" crimes like public drinking. Law enforcement in the city's subway system, meanwhile, now looks nonexistent.

Police arrested three people for trying to skip out on subway fares last week. In the same week the previous year, they arrested more than 400.

The slowdown began shortly after the deaths last month of two officers, Rafael Ramos and Wenjian Liu, who were ambushed in their patrol car by a shooter citing the recent police killings of unarmed black men. Union officials have personally blamed Mayor Bill de Blasio for contributing to "anti-police" rhetoric, and rank-and-file officers have turned their backs on the mayor at funerals for both of the slain officers. The rising tension also comes at a time when the police union is in a contract dispute with the city (as many have pointed out, the slowdown is targeting revenue offenses like parking tickets that effectively cut off money to the city).

Now, two weeks into the protest, the next big question isn't whether arrests will stay down, but whether crime will rise as a result. Here is a key paragraph far down in the Times' story:

During the first week of the enforcement declines, in fact, crime went down. But in the second week, the statistics showed an uptick: Robberies rose 13.5 percent over the week, to 361 from 318 a year ago. Murders increased to 11 for the week that ended Sunday, from seven in the same week a year earlier.

That's not enough data to draw any conclusions. But if this standoff continues, any scenario — if crime rises, falls or stays flat amid a drop in enforcement — potentially bodes badly for the NYPD. Police have cut back in particular on the kinds of minor offenses targeted by the "broken windows" theory of policing (public urination and turnstile jumping are classic examples). But if crime in the city simultaneously falls, or even holds steady, the NYPD could inadvertently undermine the hotly debated theory.

"Broken windows" advocates, including NYPD Commissioner Bill Bratton, have given the idea tremendous credit for making the city safer over the last two decades, even as the practice has antagonized local communities. But if serious crime does not rise while police allow minor crimes to slide by, that would offer more evidence that such aggressive policing isn't essential to maintain public order. Through their protest, New York police officers are creating a natural experiment that could add more data to this long-standing debate.

Now, what if crime rises? That alternative scenario would look arguably even worse for the police, as it would illustrate that their union is willing to sacrifice public safety in a standoff with the mayor (Conor Friedersdorf had a good take last week on why the right in particular should be miffed by this). If police officers want to feel that their city more strongly supports them, this would be a terrible way to build up that trust.

One plausible last explanation here is that police have curtailed their activity not out of protest or to prove their value to the public, but because officers truly fear their lives are at risk following the deaths of Ramos and Liu. It's hard to make that case, though, when parking tickets are down.