I visited an institute in MA for three months from another institution out of state. The purpose was to meet and learn about the work of other researchers there, provide information about my home institute, and encourage contacts and collaboration. The MA institute provided workspace for me, but I did not receive any compensation from them. I stayed in hotels and AirB&B's funded by my home institute. All my compensation came from my home institute that is out of state. Do I have any MA source income or need to file a MA income tax return?
Work income is "sourced" where the work is actually (physically) performed. Thus income from the work you performed from a location in Massachusetts is MA-source income, and therefore taxable by MA - regardless of your employer's location.
You would report that income by filing a non-resident MA tax return, in addition to your home state tax return. Your home state can tax ALL your income, including the portion you earned in MA. You'll be able to claim an "other state credit" on your home state return for the taxes paid to MA, so you won't be double-taxed.
In TurboTax, be sure to complete the non-resident state return before the home state return, so that the program can calculate and apply the credit.