Municipal governments have some freedom to govern without being under the thumb of the state or federal government. Home rule is the concept that the city has a right to operate under its own rules as a separate entity from the other levels of government.
This power comes from the Ohio Constitution.
The Ohio Supreme Court has made some rulings on the extent of home rule. But, in general, the court has left it up to interpretation. There is no clear line about where the authority ends or how much power a municipal has. The court generally approaches situations on a case-by-case basis.
The constitution allows cities to make their own rules as long as they do not conflict with existing laws. However, it is possible that city law may override state law in some cases. The state does not have the power to restrict the power of a city government. At the same time, municipal law is only applicable within the boundaries of that city.
The city has the right to set up the government and manage officials. It can make rules, create a police force and run utilities. The court has not limited the power in many cases. But it did say cities do not have the right to interfere with collective bargaining rights, prevailing wage laws, annexation and detachment of territory.
Whether the municipality has a charter is not relevant. Home rule applies to every city regardless of the state of a charter. Still, there are some limits to the power of a city government that requires lawmakers to ensure they do not go outside the confines of the power allotted to them in the state constitution.