Actually the 20 mph speed limit is a statewide law.

The following is the Arizona revised statute covering “Motorized Bicycles” and/or mopeds.
ARS Title 28 Definitions
30. "Moped" means a bicycle that is equipped with a helper motor if the vehicle has a maximum piston displacement of fifty cubic centimeters or less, a brake horsepower of one and one-half or less and a maximum speed of twenty-five miles per hour or less on a flat surface with less than a one per cent grade.
34. "Motorcycle" means a motor vehicle that has a seat or saddle for the use of the rider and that is designed to travel on not more than three wheels in contact with the ground but excluding a tractor and a moped.
A.R.S. 28-2516. Motorized electric or gas powered bicycles or tricycles; definition
A. Notwithstanding any other provision of this title:
1. A certificate of title is not required for a motorized electric or gas powered bicycle or tricycle.
2. Registration is not required for a motorized electric or gas powered bicycle or tricycle.
3. Vehicle license tax is not imposed on a motorized electric or gas powered bicycle or tricycle.
4. A motorized electric or gas powered bicycle or tricycle is exempt from the provisions of section 28-964 relating to required equipment on motorcycles and motor-driven cycles and from the provisions of title 49, chapter 3, article 5 relating to vehicle emissions inspections.
5. A driver license is not required to operate a motorized electric or gas powered bicycle or tricycle.
6. A motorized electric or gas powered bicycle or tricycle may use rights-of-way designated for the exclusive use of bicycles.
7. A motorized electric or gas powered bicycle or tricycle is not subject to chapter 9 of this title.
B. This section does not prohibit a local authority from adopting an ordinance that regulates or prohibits the operation of motorized electric or gas powered bicycles or tricycles, except that a local authority shall not adopt an ordinance that requires registration and licensing of motorized electric or gas powered bicycles or tricycles.
C. For the purposes of this section, "motorized electric or gas powered bicycle or tricycle" means a bicycle or tricycle that is equipped with a helper motor that has a maximum piston displacement of forty-eight cubic centimeters or less, that may also be self-propelled and that is operated at speeds of less than twenty miles per hour.
If that’s not bad enough local municipalities can and do draft their own laws further restricting their use. For example the city of Tempe does not allow a motorized bicycle to be operated on any street with a posted speed limit greater than 25 mph. This means I am not legally allowed to leave the street I live on.
I ride my motorized bicycle to work and back every day. It is a 21 mile round trip that passes through three different cities and one Indian reservation. Needless to say I violate all of the above laws on a daily basis; plus some I am sure I don’t know about yet. I have been stopped by the police twice. Once in Scottsdale for doing 37 mph and once in Tempe for riding on a street with a posted speed limit of 45 mph. I received a warning both times.
I have no intention of stopping or slowing down. I have spent over $1000.00 building a sturdy and safe motorized bicycle in an effort to do my part to reduce this country’s dependency on foreign oil and reduce my own personal “environmental footprint”. I believe this sort of activity should be encouraged both at the state and federal level. I understand that you can’t have people mounting 250cc motors on bicycles and traveling on city streets at 60mph but limiting the speed to 20mph is ridiculous.
I am drafting a series of letters that I intend on send to Arizona law makers and newspapers and I encourage everyone else to do the same. Now is a perfect time to push the environmental angle whether that was your reason for building a bike or not.
This is a great forum. I will post pictures and a description of my bicycle in a more appropriate thread.