The law in Arizona demands that you have an Arizona Insurance card. I have my old cars insured by out of state companies but I have an Arizona address on the policy and an AZ card in my glove compartment. I believe you will find that they may impound your car if you do not have proof of Insurance in AZ, ie a slip with "Arizona Automobile Insurance Card" clearly written on the top of it . There are several charges I had to pay that were not on my California insurance like a major theft surcharge and uninsured motorist provision and a state contribution for the uninsured pool. They asked me only once for the 7 cars I have registered here, but the AZ thing was super important. You will find that the insurance for your daily driver will be about double what it was in California, mine was. That is due to the enormous number of unregistered and uninsured illegal aliens driving and causing trouble...
Out of state insurance is not recognized, refer to question 3:
http://www.azdot.gov/mvd/faqs/script...asp?section=mi
If you feel that you can financially cover any claim that you may be involved in , then you don't need to get AZ Insurance.