You will have to attend a law enforcement academy in Phoenix. (Unless you are already certified and can get a waiver.) That lasts 16 weeks, then DPS has an Advanced Academy which is another 8-12 weeks. (It changes from time to time.) Then once you complete the Advanced academy you will be a certified peace officer in AZ. You will have to be an officer whether you want to be a pilot or an air medic, does not matter. Your time you do on the road can depend on medic needs vs. patrol officers needed. AZ is suffering from huge budgets cuts and DPS's air rescue program was cut dramatically. DPS was hiring for officers, but have ceased for now, unless you want to become a reserve officer and then try for a full-time paid position when they become available.
If you PM I can give you a ton more info and have a friend whom was a DPS air medic for 13 years.