State tax filing

Okay

I went through the turbo tax questions for both states and divided up my income.  Would I be correct to say that I do not take a credit for the AZ tax paid because I was not taxed twice, only once by Arizona.  I have tried it both ways, with credit and without.  The without credit seems more correct in my mind because the MA tax obligation is 700, but Im getting a 500 refund from AZ, so therefore I pay MA all of that AZ refund plus 200.  If I take the credit, I still get 500 back from AZ but I only owe MA 200. So in the end I end up with a refund of 300. Which does not seem in my mind to satisfy my MA tax obligation.  Unless the MA tax departed gets that money from Arizona themselves.