My Granddaughter owns her own house in McDonald, Ohio. She accepted a tenant to pay rent. There was no written agreement. The Tenant has vacated for about 3-4 weeks, is no longer paying rent but has not removed her bedroom set, clothing and other minor personal property out. To date no contact or arrangements have been made by the tenant. In addition, there is no way to contact her. Is this property now considered abandoned and the property of homeowner?

It always has been the property of the owner (your granddaughter). She was only renting to this person who left their possessions. I would consult with the tenant/landlord association in your area to find out what can be done legally to remove the tenant's possessions.