Yes, if you work in Arizona, you will have to file a non-resident tax return and pay taxes on the income you earned in the state. Create your non-resident return first in TurboTax as some resident states will give credit for taxes paid to another state. Then create your resident return for New Mexico last.
Below is information on filing a non-resident return in TurboTax:
https://ttlc.intuit.com/replies/3302052
