An Ohio sublease agreement must have the landlord's permission. This often means the tenant needs written consent to sublet the property.• Fill out the move-out checklist in the back of this booklet when you move out. You will then have the move-out checklist to compare to your move-in. The Document Center provides easy access to public documents. An Ohio sublease agreement is a contract for tenants, allowing them to create a secondary sublease with a subtenant. A sublease agreement template is used when a lessee wants to rent out a property or space within a property to an additional party in the state of Ohio (OH).