CHICAGO — Gov. Rick Snyder of Michigan appointed a new emergency manager on Tuesday to oversee the Detroit Public Schools, the fourth such state-assigned manager to lead the struggling system since it was deemed in serious financial trouble in 2009.

While the city of Detroit itself emerged late last year from emergency management and the largest municipal bankruptcy in the nation’s history, some city and state officials worry that the woes of its public schools threaten to slow efforts to remake Detroit and lure desperately needed new residents.

And so, while Mr. Snyder announced that the public schools would remain under the oversight of an appointed manager despite opposition from some school leaders who say control should be returned to the local authorities, he also made it clear that his administration and other officials would soon weigh broader changes for a school system that has wrestled with declining enrollment, disappointing test scores and financial deficits.

“This is about making sure we have a great city,” Mr. Snyder said in a news conference in a Detroit school, seated between the departing emergency manager, Jack Martin, and the arriving one, Darnell Earley.