If you are a resident of MA, you will need to include all income from both inside and outside the state on your MA resident state tax return.
You will need to file as non-resident for RI (for your RI source income only). You will also need to file a MA resident state tax return (for all income from all sources including RI). You will get a state tax credit in MA for the RI state taxes that you paid on your nonresident RI state tax return.
You will want to work on your non-resident RI state tax return first. You will then take a tax credit from your non-resident RI 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 (select "see more answer" to view the entire attachment)
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