Single family homes have one association and condos (including duplexes) are governed by several different ones. Some sections do not allow rentals, still other only allow rentals to a percentage of units.
You can start researching here:
http://suncityhoa.org (for single family homes)
http://azsccoa.org (for condos and duplexes)
Contact me if you need more information.
That is a really good question. My guess is that you are speaking specificly about a 55+ community. I would think that you can however I am sure who you rent to, should you choose to rent it... must be in the 55+ age range.