HVAC projects requiring permits include code violations corrections, along with the installation or replacement or furnaces, boilers, refrigeration equipment, fireplaces, and other HVAC products.
A permit is also required for new, extended, or repaired ductwork, hydronic lines, and control wiring.
See the link above for a permit application.
Contractors must be bonded, insured, and licensed with the State of Ohio and registered with the City of Cleveland.
Do-it-Yourselfers do not have to be registered.