Can a single mother take her child away from the father and move out-of-state?

Question Details:

I am a single mother and my residence is OH. I moved to KY into the baby's father's parent's house for a short while without filing residency and had my baby there. The baby's father signed the birth certificate but we are no longer together and I don't see him as a fit father (drugs and alcohol), so I want to move back home to OH. Do I need his consent to move back? Do we have to go to court to have a custody hearing? We were never married so I don't know what rights he has to our child.

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