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@RobertB4444 Thanks for your response. I have a few follow up questions:

1. How do I file a part-year return? Is that done separately from my regular state tax filing and is the deadline for part-year tax April 15?

2. When you say enter correct amounts into my W2s, do you mean that:
  a) In TX W2, I enter everything as is, just replace TX with MA in Box 15 and enter $0 in state income tax withheld (Box 17) and;
  b) In MA W2, I should add the state tax withheld to Box 17 and leave everything else the same?