You can register it lawfully in AZ as a non-resident. If it is currently registered in CA you may not be able to get away from paying the unsecured property tax, so it may not be worth registering it AZ. Contact the tax assessor in your county...you may be able to change the location of mooring/storage to avoid the tax. Keep the trailer registered in CA since you are a CA resident. Reg fees are:
Watercraft Size Resident Fees Nonresident Fees
0 to 12 ft. $20 $100
12 ft. 1 in. to 16 ft. $22 $110
16 ft. 1 in to 20 ft. $30 $222
20 ft. 1 in to 26 ft. $35 $259
26 ft. 1 in to 39 ft. $39 $292
39 ft. 1 in to 64 ft. $44 $330
64 ft. 1 in and over $66 $495
Everything you need to know is here:
http://www.azgfd.gov/outdoor_recreation/boating.shtml