Mayor Bill de Blasio, who ran on a pledge to reshape the department, has largely remained out of the public fray this year as the Council speaker, Melissa Mark-Viverito, has pushed for major changes in how the city handles low-level offenses, arguing that a civil process in many cases could replace a criminal one. Those potential changes would follow shifts already underway, including less stringent penalties for low-level marijuana possession.

The discussions have assumed particular resonance in recent weeks as the city pursues what it calls a new approach to community-based policing, adding nearly 1,300 officers in the hope that they will be able to spend more time getting to know the neighborhoods they serve.

The force has already stepped back from blanket enforcement of minor offenses. Summonses have fallen. Arrests are down. Street stops barely register compared with record heights in 2011. Mr. Bratton heralded the ebbing numbers as a “peace dividend,” even as he called for a larger army.

For Mr. de Blasio, it is a difficult balancing act: promoting so-called broken-windows policing while striving to reduce the often far-reaching consequences of the current approach among certain groups. The administration has also contended with weeks of unsettling headlines about rises in shootings and homicides through the first several months of the year. (Crime figures in recent weeks have been more encouraging.)

For two decades, police officials viewed the enforcement of minor infractions as a way to prevent crime and violence. “Quality-of-life enforcement works to reduce crime,” wrote Jack Maple, a primary architect of the approach during Mr. Bratton’s first tour as police commissioner in the 1990s, “because it allows the cops to catch crooks when the crooks are off duty, like hitting the enemy planes while they’re still on the ground.”

On the issue of public urination, enforcement need not be evenhanded, according to Mr. Maple. In his 1999 memoir, “The Crime Fighter: Putting the Bad Guys Out of Business,” he wrote that “Wall Street analysts doing Jell-O shots” on Madison Avenue may be just as likely to urinate in public “as a crew of robbers drinking malt liquor” in East New York, Brooklyn. “But only one of those groups is likely to include somebody who’s relaxing after a long day of robbing,” he added, suggesting that officers should more heavily enforce the law in those areas.