A. Any county license tax imposed pursuant to this chapter shall not apply within the limits of any town located in such county, where such town now, or hereafter, imposes a town license tax on the same privilege. If the governing body of any town within a county, however, provides that a county license tax shall apply within the limits of such town, then such license tax may be imposed within such towns.
B. Notwithstanding the provisions of subsection A of this section, in a consolidated county wherein a tier-city exists, any county license tax imposed hereunder shall apply within the limits of any tier-city located in such county, as may be provided in the agreement or plan of consolidation, and such tier-city may also impose a tier-city license tax on the same privilege, provided that the combined county and tier-city rates do not exceed the maximum permitted by state law.