Toni,
Ohio Revised Code 5321.15 says that you can't seize T's stuff "for purposes of recovering unpaid rent" except by court order. Is his stuff valuable? If so, get a court order allowing you to seize his stuff & sell it. Otherwise, it appears you can simply stick his stuff out on the curb for him to pick up at his convenience. After several weeks, I think the property is abandoned. You could also move the stuff to storage, as long as you are willing to give it to T if he shows up before you get a court order allowing you to sell it. You may not be able to charge T for the moving costs or storage fees, though.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.
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