In the My Info section of the TurboTax program you should have listed your resident state as of 12/31/2019. You should have also indicted that you lived in another state in 2019 and the date you move to your resident state.
You will file a Arizona part year personal tax return reporting your income earned in Arizona while a resident. If you overpaid your state income taxes then you will get a refund for the overpayment.
New Hampshire does not have a personal income tax so you do not file a NH state income tax return for the wages earned while a NH resident.
