You need to file a Part-Year resident form in AZ (140PY). AZ will tax you on money earned before you moved to UT. If you made money from property (e.g. a rental home) or a business in AZ even after that, AZ will tax that also.
For 2017 you will also do a UT part-year resident form. UT will tax you on money earned after you moved to UT (and any money earned at any time from property or business in UT).
You will have to check the UT part-year instructions to see if you need to file. You might need to file even if you owe nothing because the form is where you figure out how much income goes to your AZ time and how much goes to UT. The resulting income might put you below the filing requirement or it might not. Check the instructions or work out the form.
For 2018, if you stay in UT (and don't work in AZ), you should file a UT resident form and no AZ form.
https://incometax.utah.gov/instructions/nonresidents
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