Do I have to file a Hawaii state tax return if I work remotely for the state of Hawaii but live in Arizona? Hawaii took taxes out of my pay.

It depends. You will have to file a resident Arizona return and a nonresident return for Hawaii if Hawaii state taxes were withheld. If your employer withheld Arizona state taxes, then you would only need to file an Arizona resident return. 

Per the State of Hawaii, nonresidents should report personal services performed in the State of Hawaii. Since you worked from your home state of Arizona, then you have $0 amount of sourced income in the State of Hawaii. However, you would have to file to get a refund of your Hawaii state taxes withheld. 

If you do have to file a nonresident return for Hawaii, the first thing you want to do is make sure you've filled out the Personal Info section correctly:

1. With your return open, select My Info in the left-hand menu.
2. Then, on the Personal info summary screen, please make sure your resident state (as of December 31, 2020) listed under your name is correct.
3. Then, scroll down to Other State Income, and select Edit.
4. At the Did you make money in any other states? question, answer Yes and make sure your other nonresident state is selected from the drop-down.
5. Select Continue to return to your Personal info summary.
6. Click on State on the left hand side. 
7. Add the state of second state as a non-resident. 
8. Follow the on-screen instructions.