“Tell me what race dominates in those communities that get emergency managers?” said Hubert Yopp, the mayor of Highland Park, Mich., which is 93 percent black and in past years has had an emergency manager. “People have a very real reason to question what that’s about. It would be one thing if the emergency managers worked with the local governments to make things better. But it’s about having dictator power in the city. The locals have no say.”

Some form of state-over-locality oversight exists in about 20 states, with laws allowing for an appointed manager or board to advise distressed cities and school districts, said Eric Scorsone, the director of the Center for Local Government Finance and Policy at Michigan State University.

Central Falls, R.I., went into receivership for a year before it declared bankruptcy in 2011. New York City was steered away from fiscal collapse in the 1970s with the help of a financial control board.

In New Jersey, Camden was under state supervision for seven years until 2010, while the Newark Public Schools are still under state control two decades later. Philadelphia’s public schools were taken over by the governor in 2001.

This week, Gov. Bruce Rauner of Illinois, a Republican, said that he favored state oversight of the Chicago Public Schools, a measure that stands little chance of passing in a legislature controlled by Democrats.

But Michigan’s law is among the nation’s most far-reaching, said Mr. Scorsone, a critic.

“When you have one voice, you essentially don’t have checks and balances in a democracy,” Mr. Scorsone said. “The outcome in Flint has revealed some significant flaws in the process.”