Yes, both states tax your income. Your resident state (CT) is allowed to tax all of your income no matter where you earn it, and your nonresident state (RI) is allowed to tax any income you earned in the state. However, to reduce the effects of double-taxation, your resident state will allow you a credit for the tax you must pay to the nonresident state, up to the amount of tax you would pay in the resident state on the same income.
For this reason, prepare the Rhode Island return first, so that the amount of tax credit can be transferred over to the Connecticut return. Likely, if you owe anything in Connecticut, the tax credit will reduce and possibly even eliminate any amount you might owe (but you will still be required to file a CT return).
You may find this FAQ helpful: https://ttlc.intuit.com/replies/3302052
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