Probably, but things will go smoother if you have a AZ workers compensation attorney before you leave the state.
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Probably, but you would need to file a "request to leave the state" with the Arizona Industrial Commission to get your out of state bills covered, and keep any compensation you may be entitled to in effect. You may also want to file a "request to change doctors" once you find a doctor in your new locale. The Commission's number is 602-542-4661.