(A) No political subdivision, district, or agency of the state may adopt an ordinance or rule that requires contractor registration and the assessment of a registration or license fee unless that ordinance or rule also requires any contractor who registers and pays the registration or license fee to be licensed in the contractor's trade pursuant to this chapter.
(B) Except as provided in division (A) of this section, nothing in this chapter shall be construed to limit the operation of any statute or rule of this state or any ordinance or rule of any political subdivision, district, or agency of the state that does either of the following:
(1) Regulates the installation, repair, maintenance, or alteration of plumbing systems, hydronics systems, electrical systems, heating, ventilating, and air conditioning systems, or refrigeration systems;
(2) Requires the registration and assessment of a registration or license fee of tradespersons who perform heating, ventilating, and air conditioning, refrigeration, electrical, plumbing, or hydronics construction, improvement, renovation, repair, or maintenance.