The Brooklyn district attorney’s office will stop prosecuting people arrested on charges of possessing small amounts of marijuana, according to a confidential policy proposal that the district attorney, Kenneth P. Thompson, sent to the New York Police Department this month.

The policy is part of a broader push on the part of Mr. Thompson, who took office this year, to look at alternatives to court for low-level offenders. His office is also participating in a task force looking into placing 16- and 17-year-olds who commit low-level, nonviolent misdemeanors, like scrawling graffiti or aggressively riding bicycles on sidewalks, into a short behavioral program, rather than the court system.

Defense advocates and community groups across the nation have been pushing the judicial system to rethink the traditional approach to handling small offenses.

Yet the moves have created tension between Mr. Thompson and police officials. The police commissioner, William J. Bratton, has been a proponent of the “broken windows” theory of policing, which holds that arrests for small violations help prevent larger crimes. Mr. Bratton espoused this theory when he was the commissioner under Mayor Rudolph W. Giuliani in the 1990s, and, after returning to the department this year, has been directing officers to go after subway panhandlers and peddlers.