(a) The governing body of a municipality and the commissioners court of a county may adopt ordinances or rules under Section 826.014 or 826.015 requiring the registration of each dog and cat within the jurisdiction of the municipality or county.
(b) A dog or cat may not be subject to dual registration.
(c) The enforcing agency may collect a fee set by ordinance for the registration of each dog or cat and may retain the fees collected. The fees may be used only to help defray the cost of administering this chapter or the ordinances or rules of the enforcing agency within its jurisdiction.