If you filed the HI form HW-4 with that employer, indicating in the part 3 checkbox that you were a "Nonresident Military Spouse (not subject to withholding)",...then you shouldn't have to file HI at all.
Just AZ.
AZ Pub 705 indicates the following:
Q13. If I am an Arizona resident who is living in another state solely to be with my active duty military member spouse, and I have a job in that state, what should I do if my employer will not agree to withhold Arizona income tax from my wages?"
"As an Arizona resident, your income earned in another state is subject to Arizona income tax. If your employer will not withhold Arizona income tax from your wages earned in another state, you may make voluntary estimated income tax payments to Arizona even though you may not be required to make estimated payments to Arizona. Use Form 140ES to make Arizona estimated income tax payments. Individuals that meet an income threshold ($150,000 for married taxpayers filing a joint return) are required to make Arizona estimated payments. For more information about Arizona estimated income tax payments, see Arizona Form 140ES."
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
