Mr. Bratton described the shift in internal discipline as part of a broader push to change police culture. By breaking with his predecessor’s harder line on low-level misbehavior, he said, he hopes to change officers’ attitudes about their jobs and, in the process, their attitudes about the people and neighborhoods they serve.

“I’m practicing community policing on the cops,” he said in an interview about his effort to reshape how the department polices itself.

For Mr. Bratton, the new approach is a key test of his second stint as New York’s police commissioner, which began in the shadow of the stop-and-frisk practices employed during the Bloomberg administration. It comes at a time when police departments across the country are under pressure to address the anger and frustration that have fueled antipolice protests for over a year, feelings that were stirred again by the arrest of Mr. Blake, who is biracial, by a white plainclothes officer, James Frascatore.

But treating officers differently does not guarantee they will treat civilians differently, and shifting to a more discretionary system of discipline presents risks. Many past police corruption scandals grew out of a culture that was more tolerant of officers’ misdeeds, and some students of that history say strict supervision and consistent enforcement are essential to deterring serious graft.

“If the rule makes sense, then the rule should be there and be applied to everyone,” said Milton Mollen, a former state appellate judge who led a commission that investigated police corruption in New York in the 1990s.

A ‘White Socks’ Problem

Like police commissioners before him, Mr. Bratton is facing high-profile, high-stakes disciplinary matters. Before Mr. Blake’s arrest, by an officer with a history of civilian complaints, the commissioner was already weighing the actions of officers and supervisors involved in the fatal encounter with Eric Garner on Staten Island in July 2014. And this summer, 19 officers in the Bronx were accused of downgrading criminal complaints, to make crime levels in their precinct appear lower than they actually were.