Yes, depending on the size or need of the city, black neighborhoods sometimes had their own municipal services, not just police departments, but fire stations as well. Many of these hires came as a result of the widespread growth of cities, and ethnic precincts. Chicago would hire its first African American officers in 1872, largely restrained to the black portions of the city. Boston would do the same in 1878, and New York in 1891 and 1911. Their first officer, Wiley Overton was hired by the city of Brooklyn, and when the five burroughs were incorporated in 1898, the city of New York would officially hire another black officer in 1911, Samuel J. Battle. Officer Battle would go on to become the first Black Police Sergeant, Lieutenant, and Parole commissioner before his retirement in 1951. It should be noted that Battle heavily assisted in calming down the 1943 Harlem Riots between Blacks and Whites.
Something also interesting of note, is that like many white police departments in that Era, the Black Harlem PD paid tribute to various mob bosses. As I mentioned here. Mob boss and "Madame" Stephanie St. Clair kept a tight grip on the Harlem precinct as well as the illegal business going on in the section of the city. The integration of Police Forces, as in many other facets of American life, stalled in the 1930's and 1940's, though it began picking up again in the 1950's as the walls of Jim Crow came tumbling down.
A note on sources
Sourcework for this field is particularly tricky as many of these men's files have been lost to time, additionally the scholarship is highly regional and divided by era. Deep academic study on the Black police officer only began to pick up in the 1960s and 1970s as a response to the Civil Rights Movement and Black Nationalism.
[A brief oral history taken from Officer Samuel J. Battle in 1960] (http://c250.columbia.edu/c250_celebrates/harlem_history/battle.html)