Legal Question in Landlord & Tenant Law in Ohio

In Ohio, the answer is yes. Ohio Revised Code Section 5321.04 defines the landlord's duties to the tenants of residential rental properties. It makes the landlord responsible for the HVAC systems in the rental property and creates no exceptions which make the right dependent upon whether or not the tenant is in good standing on the rental obligations.

However, as a practical matter, if you don't have a solid defense to the eviction, you would likely be removed from the rented premises before the law would require the landlord to fix it.