You do not have an obligation to talk with the police at any time. You have the right to remain silent and the right to have an attorney present during any questioning. Those are your Constitutional rights. In Kentucky and Ohio, you do have to tell police your name, but that is all you need to tell them.
If police try to question you, the best strategy is to politely inform them that you wish to assert your Constitutional rights to remain silent and speak with an attorney. Law enforcement must advise you of these rights if they arrest you, but not before an arrest. But you have those rights all the time and can assert them under any circumstances.