The lead plaintiff in the case is David Floyd, a medical student who was stopped twice, once in the middle of the afternoon when he was in front of his home in the Bronx, according to the suit.
"We need somebody to look over the shoulder of the police department, not in an overly aggressive way, but in a limited way to make sure that this practice is being done in a constitutional fashion," said plaintiff attorney Jonathan Moore.
City Council Speaker Christine Quinn said this week that council members have reached a "broad agreement" on a bill to have an office within the city's Department of Investigation that would be allowed to subpoena police officials and documents.
The trial is expected to last four to six weeks and is scheduled to reconvene on Wednesday. The outcome will be decided by U.S. District Judge Shira A. Scheindlin.