Yes, as long as you enter the correct information into TurboTax when you enter in your W-2. Enter your information as reported on your W-2 for Box 14. Then, in the Box 14 "Category" dropdown on TurboTax, select RI TDI. In Box 15, make sure that RI is the state where the income was earned. These entries allows TurboTax to give a Mass credit against the RI TDI withholding.
You can compare this by taking the W-2 Box 17 RI tax withheld amount, subtracting the RI refund (make sure you prepare the RI return first before preparing the MA return for this reason), and then adding the TDI amount in box 14. This amount should equal the MA credit for taxes paid to another state. Please see screenshots:
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