In general, you pay income tax on all sources for your RESIDENT state.  A nonresident only pays tax on income earned in the nonresident state.  To avoid the double taxable taxation, the resident state gives a credit for taxes paid to another state. 

I guess my confusion might be the way my daughter is getting her withholding done & the way it's being processed. She apparently didn't fill out the form as a non resident & is getting Arizona tax withheld, not Oregon. So, essentially she is getting a refund of the taxes paid for her NR Arizona return, but has to pay taxes on her OR resident return. So since she is getting a fu refund on her NR AZ return, the credit is zero. Is that correct?

@MaryK4 @BillM223 

Thank you! I'm pretty sure she already did the Oregon return, since the info was there from last year, so I'll have her delete it & do the NR AZ, first.

If the return is done Online and it has not been paid for, then she can delete the state by following this FAQ. 

But note this:

"If you don't see the option to delete your state (you'll probably see Edit instead), you've already paid your TurboTax fees (including the state fee) or registered your free version while the state was on your return. If you've done either of these things, you can't delete your state return."

See if she knows what the status is (like can she delete the state) and come back and ask what to do of she can't delete the state.

@BillM223 

Zero is showing on line 61, but the amount is showing on lines 67 & 68. I am not sure what I am doing wrong. I have deleted the OR return for now.

Those credits are tricky!  You must do the non-resident AZ return first to calculate a tax liability.

Then you do the resident OR state and it gives you credit based on the tax liability you just calculated in the non-resident AZ state.

If they are not done in this order, the program may not calculate your resident state correctly.

You may want to delete everything state and start fresh with AZ.

Revisiting this as I've now deleted the Oregon return & started from scratch. All was looking good until the review which said I can't put Arizona as a state for credit paid to another state. It appears as though since she is a full year resident of Oregon (bc she's just attending college in AZ) that she is not able to claim this credit. At this rate it looks like a refund for those taxes paid to Arizona, and a much larger tax due to Oregon with no credit for those taxes already paid to Arizona. 

At this point, i would suggest contacting phone support to review your tax return to determine why you aren't receiving a credit for your taxes paid to Az. Please select this link for information to contact phone support.