I moved from MA to AZ at early December last year for work and was living in a hotel until early this year. Initially the tax was withheld for both states, but was adjusted after telling the HR (which happened earlier this year). I have received the w-2c with box 16 corrected to 0 for MA while the part for AZ remain unchanged.
You will file part-year in both states and allocate based on the period of residence for each state. In the "My Info" section indicate you lived in AZ on 31 Dec and answer "Yes" you lived in another state (MA). Enter the date you moved to AZ. In the "Wages & Income" section enter the form W2 just as you received it (corrected version). Finally in each of the state interviews you will allocate each of your income sources based on you time in each state (i.e. 11/12 months wages in MA).