Found some info (search) from Scottsdale where this guy was really hassled/ticketed twice by the same cop. He was supposedly clocked going over 20mph, and as Finfan posted, moped law then applies.
I'm up in Prescott, and so far, so good. I've had several officers admire my bikes and ask "how fast will that thing go?". Of course, my reply is "20 mph". I can only hope that things stay the same here, because according to ARS 2516, local authorities can adopt an ordinance that "regulates or prohibits" our bikes. They can not require registration or licensing of the bike, but as in Tempe (can't use on a street with a posted speed limit over 25 mph, in addition to other restrictions) pass local laws that make it all but impossible to use on the street.