Kentucky has 173 public school districts, 53 of which encompass only one or more cities. However, even these "independent" school districts - with a city in their name - are not operated by Kentucky cities. Kentucky voter elect school board members, similar to city elected officers, to make decisions for their public school district. These school boards set the tax rates and approve the budget for the school system.
Even though city leaders don't have control over their local schools, they often work together with the local school district superintendent, school principals, and teachers. After all, schools need good roads and sidewalks for students to get to them, crossing guards and school resource (police) officers to improve safety, and many other city services.