The state of Arizona has no mandatory helmet use law for bicyclists; there are a few municipalities that have their own rules.
Specifically, I believe this is a correct list at bhsi.org, current as of mid-2011 (and I see nothing in the pipeline):
|Municipality||applies only to||Year Enacted|
|Pima County||Under 18||1995|
|Sierra Vista||Under 18||1995|
Noteworthy: as I scan the whole list I don’t see any state that mandates adult helmet use, only various ages of minors.
In case you were wondering, Motorcyclists…
According to iihs.org there is a state law for under-18 year-old motorcyclists — including “motor driven cycles” (< 5hp). The statute is 28-964; and a quick read says that “motor driver cycles” do not include either mopeds or “motorized bicycles” but I’m not really sure. Here is some material from www.usff.com/hldl/hlstatutes/arizonahl.html (I removed the link, if you want to visit the site, copy and paste it… as of Feb 28, 2013 this link is listed as “may harm your compter” by google), and anti-motorcycle mandatory helmet law site.