Legal Question in Landlord & Tenant Law in Ohio

In Ohio, relations between residential tenants and their landlords are covered by both the lease agreement and Ohio Revised Code Section 5321. R.C. 5321.04 states that the landlord is responsible for putting and keeping the premises in a fit and habitable condition with regards to any HVAC (Heating Ventilating and Cooling) system.

Here is where you can go for a full explanation of your rights when a landlord will not meet his duty to fix things around the rental unit: http://www.ohiolandlordtenant.com/faq1.html

You should also note that R.C. 5321 has a section which says that if the lease and the law conflict (in your case the lease may say you have to pay for fixing the furnace but the law says that he does), then the law wins and contrary terms in the lease agreement will simply be ignored by the Court.