If you are using the Desktop version of TurboTax, and you need to redo a state return, you can delete the return within TurboTax and run it again. Deleting the return doesn't delete the program from your computer.
The order in which the state returns are completed makes a difference in many cases, as your resident state may offer a credit for taxes paid (not to be confused with taxes withheld) to another state, and in that case you would need to have calculated the tax liability for the other state. You also need to determine whether the two states have reciprocity agreements, which may be able to eliminate the need for the second state return unless you have taxes withheld in the second state.
See this article for information on states with reciprocity agreements. Massachusetts and Rhode Island don't currently have a tax reciprocity agreement. An employee who is a resident of Rhode Island is subject to Rhode Island withholding for wages earned in Rhode Island. If a Rhode Island resident works in another state, such as Massachusetts or Connecticut, the wages will be taxed in the state where the wages are earned.
See also this TurboTax article and this one on multiple-state situations.
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