It depends.
If you lived in Massachusetts all year:
- all of your income will be taxed in Massachusetts - regardless of where you earned it
- you'd file a nonresident Rhode Island return and pay tax on the income that you earned there
- Massachusetts will give you a credit for the tax that you paid to Rhode Island so that you aren't paying tax on the same income twice
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If you lived in Rhode Island for part of the year and in Massachusetts for part of the year:
- only the income that you earned while living in Rhode Island would be taxable to Rhode Island
- only the income that you earned while living in Massachusetts would be taxable to Massachusetts
- you would file a part year return for each state