The New York City Police Department has a long history of violating constitutional rights by stopping, questioning or frisking people on the streets without legal justification. The city has steadfastly denied that the detentions — made under its increasingly unpopular stop-and-frisk program — have been based on race.

But that claim is being challenged in Floyd v. the City of New York, a federal class-action trial in Manhattan, where witnesses including police officers are arguing that the department does, in fact, use race as the basis for stopping and frisking hundreds of thousands of citizens a year.

This week, the court heard a troubling recording secretly made last month by Officer Pedro Serrano, of the 40th Precinct, in the South Bronx. Mr. Serrano is one of a handful of officers who began tape-recording conversations with their colleagues or superiors to document what they saw as wrongdoing.

In the recording, Deputy Inspector Christopher McCormack is heard urging Mr. Serrano to stop, question and, if necessary, frisk “the right people at the right time, the right location.” When Mr. Serrano asked for clarification about who the “right people” were, the inspector replied: “The problem was, what, male blacks.” He continued, “And I told you at roll call, and I have no problem telling you this, male blacks 14 to 20, 21.”

On its face, this would seem to violate the Fourth Amendment, which protects citizens against unlawful search and seizure. Police officers can legally stop and detain a person only when they have a reasonable suspicion that the person is committing, has committed or is about to commit a crime.

The trial court also heard this week from Officer Adhyl Polanco of the 41st Precinct, who had taped proceedings in his station house. Mr. Polanco testified that officers were subject to a quota system, which required them to write more summonses, make more arrests and create stop-and-frisk encounters. He said that his superiors wanted “20 summons and one arrest per month.” The plaintiffs argue that a quota system put officers under pressure to make unconstitutional stops.

The trial is expected to last six weeks. But the testimony has already pointed to disturbing conduct by the police command and a profound indifference to the constitutional rights of the city’s citizens.