(a) The governing body of a municipality may adopt ordinances or rules that establish a local rabies control program in the municipality and set local standards that are compatible with and equal to or more stringent than:
(1) the ordinances or rules adopted by the county in which the municipality is located; and
(2) the program established by this chapter and the department rules adopted under this chapter.
(b) Municipal ordinances or rules adopted under this section supersede ordinances or rules adopted by the county in which the municipality is located, this chapter, and the department rules adopted under this chapter within that municipality so that multiple enforcement will not occur.