Even though state tax was not withheld in your new state, you will still need to file and pay tax to the new state. You will have also overpaid to Arizona, and will be due a refund of the amounts that are overpaid.
You should file your part-year returns in both states now. This will allow for time for you to receive your refund from Arizona in time to pay the amount due to your new state for taxes not withheld.
If you haven't done so already, be sure to have your employer update your withholding for 2020 so that next year things are a little easier for you!
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