There is a special law applying specifically to bicyclists; it often gets repeated as
You must have at least one hand on the handlebars at all times
While this is the law in some places, e.g. Utah (41-6a-S1112); the law in Arizona actually reads:
ARS 28-816. Carrying article on bicycle
A person shall not carry a package, bundle or article while operating a bicycle if the package, bundle or article prevents the driver from keeping at least one hand on the handlebars.
So, while you should and must ride under control for safety’s sake, it’s not intrinsically illegal to ride with no hands.