The family of a black Tennessee man who was shot and killed by a white police officer in Nashville in July sued the officer and the city on Monday, saying that its Police Department discriminates against black people and that its officers are too quick to use lethal force.

The 34-page suit, filed in United States District Court, states that Officer Andrew Delke of the Metropolitan Nashville Police Department had internalized a police culture of “fear, violence, racism, and impunity” that in part motivated his fatal shooting of the man, Daniel Hambrick, 25.

The lawsuit, which seeks $30 million in punitive damages, said police officers in Nashville are trained to be paranoid and believe that “without constant police vigilance and the threat of police violence Nashville’s black community would degenerate into violence and anarchy.”

Joy S. Kimbrough, who is representing Mr. Hambrick’s family, said at a news conference in Nashville on Monday that what was done to Mr. Hambrick was “beyond some misconduct.” She added, “We want the responsible party to be responsible for their actions.”