First, be sure to complete all federal information, then CT's return and then MA. Be sure to enter your W-2s as they're reported to you and that will account for your withholding. When you start each state, all of your information will transfer. You'll file part-year/non resident return in each state.
Each state will ask you questions, based on the income allocable to that state and their state rules. If you basically worked in CT the entire time, then CT will tax all of your income. You can get complicated and leave out the dates you worked in MA, but if you don't have detailed records, just let CT claim all of your income. Them, MA will tax all of the income you earned while a resident in the state and you will have to tell the software this amount. You can figure this out by looking at your W-2s.
However, MA will give you credit for the taxes you paid to CT, so that you aren't double taxed. This is why you must complete your CT return in the software first. If you didn't, you'll need to delete the state and re-update them in order. See instructions below: https://ttlc.intuit.com/replies/3301384
