Roommate/father Squatting

Hello! Around two years ago, my (27F) father (69M) called me and told me that he was on the verge of being homeless. We have always had a strained relationship but trying to be a good daughter and since my lease was almost up, I decided to help him out and we moved into a 2 bedroom apartment with both of our names on the lease. We had a verbal agreement that he could take the year and get his life in order and find his own place. Well, two years have come and gone now and he’s made no attempt to find somewhere else to live. I pretty much figured this would happen, but I wanted to give him the benefit of the doubt that he wouldn’t take advantage of me because he’s my dad. Of course, I was wrong. Now, our lease is coming to an end in August of this year. I am NOT renewing it, I have made it absolutely clear to him that the lease will be up and I will be moving to a different state (partially to get as far away from him as possible). I intend to give written notice to the landlord at the 60 day mark. He is fully aware that he needs to vacate the apartment by August. However, in the last few days he has started making comments that he is just going to stay in the apartment and be a squatter, and that he doesn’t want to move. Living with him has put me into an incredibly dark headspace and I cannot go on living with him, and I am fully aware that this is a manipulation tactic. I have no idea what to do now. What legal trouble do I face if I move out when the lease is up and he remains in the apartment as a squatter? Both of our names are on the lease. This is in Ohio. I know we are both responsible to pay the rent. Will it lead to an eviction on my name if they have to remove him as a squatter when I am already gone to another state?