Because you have RI source income (for the 2 months that you worked in RI) but live in MA, you will need to file a nonresident RI state income tax return and a resident MA state income tax return.
The fact that you did not have any RI state withholding will just mean that you may owe taxes on your RI nonresident state income tax return and may get a refund (or owe less) on your MA resident state income tax return
You will be taxed on your wages both where they are
earned (RI)(2 month's worth) and in your home state (MA). However,
you will get a tax credit for the RI taxes (nonresident state) you paid with your RI nonresident state income tax return on your
MA state income tax return (resident state). This is how the states avoid double
taxation by allowing a state credit in your home state. Towards the end of
the state information, you should see a list of other state tax credits. If RI is not listed, you can add the RI state income taxes paid as a credit in this section. (Just
remember that you will not get a tax credit on your nonresident state return for taxes
that you pay in your resident state)
You
will need to file as nonresident for RI to report your RI source income only (If your employer did not allocate your income between the 2 states, you will need to allocate your income between the 2 states based on the number of days worked in each state). You
will also need to file a MA resident state tax return (for all income from all
sources including RI). .
You
will want to work on your nonresident RI state tax return first. You will then
be able to take a tax credit from your nonresident RI state return on your resident MA state
tax return. (Please note that you will only get a tax credit for your RI taxes
up to the amount of MA taxes that would have been paid if the income was earned
in MA).
Just
follow the TurboTax guide when working on your states (remembering to do your
non-resident state return first) and TurboTax will do all the calculations for
the credit to your resident states return
Here
is additional information about filing in multiple states
https://ttlc.intuit.com/replies/3300797
