The Non-MA Portion of Income is the amount of money you earned when you were not a resident of Massachusetts. In your example, the Non-MA Portion is $7,000 ($1,000 NY + $6,000 NH).
You will also have to calculate your Non-Massachusetts portion of Social Security and Medicare tax on the screen "Non-Massachusetts Portion of Deductions."
Figure the NY and NH portion of W-2 Box 3 and multiply that by 6.2%. Multiply Box 5 by 1.45%.
New Hampshire does not have an income tax. You will not have to file a return unless you have interest and dividend income over $2,400 ($4,800 for joint filers).
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