Respectfully, ***** ***** to disagree with the assertion that the homeowners' association is likely subject to the Americans With Disabilities Act, because that regulation addresses only entities that offer a 'public accommodation' such as a restaurant, retail story, etc. Homeowner's associations would not generally qualify under this criteria.
However the Federal Fair Housing Act is fully applicable and requires homewoners' associations to comply with reasonable accommodations. Assuming the sign indicating a handicapped person is in the vicinity or designating a handicapped parking space on a public street, then clearly you should not be harassed in anyway or threatened with penalties from the homeowners' association, which are most likely of no legal force. So I agree with the earlier advice, and firmly request the association desist in harassing you: I recommend doing this in writing by certified mail or return recept request. (a pain, I know, but proof of delivery may come in handy if they decide to get snarky and escalate this). If necessary, get a lawyer to draft a something simple -- or go only and search for a "cease-and-desist" form letter and do it yourself! (You will probably need to modify the language to suit your specfics)
You mentioned that some streets in the subdivision had different designations as to being public or still under the private control of the homeowners' association: that may be the case, depending on your particular housing subdivision and Nevada law. Generally, once a subdivision section if fully developed including paving and other municipal requirements, the developer -- or association -- petitions the municipality (or county) to assume control, and therefore pay for maintenance.
Where the road is in a section not fully developed -- say the road is still unpaved -- or in a section the association want to retain as private, then usually the municipality does not take control.
You local public works office can tell you with a simple phone call.
In any case, it should not be an issue for you, as you should be protected under Federal Fair Housing Action, and state protections.