momma_blue,
Yes! Indeed, the Arizona income tax booklet
https://azdor.gov/file/12173/download?token=aErrumSx
specifically states on page 15:
NOTE: If you did not claim a dependent who is a student on
your federal return in order to allow the student to claim a
federal education credit on the student’s federal return, you
may still claim the dependent on your Arizona return.
For more information, see the department’s ruling, ITR 05-2,
Will Arizona Allow a Dependent Exemption When a Taxpayer
Does Not Claim Federal Exemption in Order to Claim the
Education Credit?
While technically there is a provision that allows your dependent to claim a federal tuition credit, from a practical matter it seldom works out. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working . She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)