My question involves an eviction in the state of: Ohio

My boyfriend and I were living together, he is not on the lease, and had not paid any rent. After things went sour, he moved out and had been gone for 17 days. I didn't worry about an eviction notice, as he moved out promptly and even told me I could keep some of his things if I didn't sue him for the rent he agreed to pay.

However, he showed up again tonight drunk and broke in the back door (although he claims he used a key, but I have all the keys) and refused to leave. I called the police but they said he is still a legal tenant. Is this true even though he moved out and relocated to a new city and hasn't been living in the premises for 17 days?

Any help is greatly appreciated!