Still, it is an accepted tenet of community policing that when departments reflect the communities they serve, they have an easier time building trust and defusing, rather than escalating, tense situations.

In Maple Heights, some residents said they would like to see more black officers, while others said that it was the attitude, experience and training of the officer, not race, that mattered. Chris Turney, a home renovator who lives with his wife and two daughters, said it was more important for officers to live in the city. All but one do not.

“The police come here, they do their jobs, they don’t try to get to know anybody,” said Mr. Turney, who is black. “The police don’t wave.”

Other residents drew a contrast between police attitudes in Maple Heights and neighboring Bedford Heights, where three-quarters of the residents, and nine of 28 police officers, are black. “Bedford’s not going to do you like Maple,” said Carlos Walker, 41, who is black. “You have to do something real stupid for Bedford. Maple, soon as they get behind you, you sweating.”

In her 11 years as an officer in Bedford Heights, Detective Ericka Payne, who is black, has often provided backup on calls in Maple Heights. “There are definitely differences in the ways the departments interact with the outside community,” Detective Payne said. “We try to be a little bit more community oriented. Because we are a little bit more diverse, we understand those dynamics and maybe have a little bit more ease dealing with that.”

Several Maple Heights officials said the diversity of the police and fire departments had never been a major issue. It is hard to find qualified candidates of any race, said John C. Popielarczyk, who has been with the Maple Heights Police Department since 1990 and the acting police chief since May.