When you have a two (or more) state situation, you are given a chance, in the state interview to manually allocate each piece of income (including wages) to each state.
I'm not personally familiar with the AZ software, but in some state programs you must allocate the wages at the W-2 screen. You may have to use a work around to get TT to allocate your wages. At the w-2 screen split the boxes 15-17 W-2 info into 2 lines. On the 1st line leave AZ in box 15 but change the box 16 amount to what you earned in AZ ; leave the AZ withholding in box 17. On the 2nd line put NH in box 15 and the NH wages amount in box 16; leave box 17 blank.
