If you paid Connecticut tax on your unemployment income, you can file a Non-Resident state return there. You may get a refund, depending on the amount of your UI income, and the amount of tax paid.
Here's more info on How CT Taxes Non-Resident Income. Prepare your non-resident return first. Click this link for instructions on How to File a Non-Resident State Return.
New York will tax all of your income, but gives you a credit for tax you paid to CT, so you're not double-taxed.
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