In general (because I don't have all your specifics), you will do the following
- In Personal Info or My Info, report that you live in Connecticut, but add that you lived in a second state, Massachusetts
- Enter the date you move
- Enter your Massachusetts data first
- Then enter your Connecticut data
The state where you live gets to tax you. The state where you work gets to tax you. The resident state will grant (normally) a tax credit for taxes paid to the nonresident state, to alleviate double taxation.