A pool needs a permit to be built, but once built, as far as I know, there are no additional taxes or fees. Although, I'm not 100% sure how local governments use the knowledge of a pool in assessing your property taxes. As far as I can tell, they don't use a pool in establishing your property taxes, and rather use lot size and property size, but perhaps a pool does come a little into the equation.
You might check maricopa.gov to see if there's any mention of pools from the assessor's office.
For sure, there is not an explicit pool tax.