Yes, generally, states tax RESIDENTS on all income and tax NONRESIDENTS on state source income. The resident state gives a credit for tax paid to the nonresident state so the income is not double taxed. She must report all of the income to Ohio and the income she earned in RI to RI.
Some states do not require filing a tax return if no tax is due, unfortunately, Rhode Island does:
"Every nonresident individual required by the laws of the United States to file a federal income tax return who has income derived from or connected with Rhode Island sources must file a Rhode Island individual income tax return."
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