FLINT, Mich. — A criminal investigation into this city’s water crisis reached into the top ranks of supervision over Flint on Tuesday as Michigan officials announced felony charges against two former state-appointed emergency managers, accusing them of fixating on saving money rather than on the safety of residents.

The managers, who were appointed by Gov. Rick Snyder to lead Flint out of fiscal distress, were charged over their roles in the public health crisis prompted by the city’s switch to a new water source, as well as the delays in responding to residents’ complaints as they suffered the devastating effects.

Announcing the charges at a banquet center not far from the Flint River, Bill Schuette, the state’s attorney general, described “a fixation on finances and balance sheets” as at the root of what happened in Flint, where the water has been tied to the lead poisoning of children and the deaths of 12 people from Legionnaires’ disease.

“All too prevalent in this Flint water investigation was a priority on balance sheets and finances rather than health and safety of the citizens of Flint,” said Mr. Schuette, a Republican who is seen as a possible candidate for governor in 2018.