For the time you lived in CT and received unemployment from NY, you will be taxed by both states on it. As a non-resident, NY taxes any income you receive related to a trade or business previously carried on that state.
CT taxes all income you receive while a resident of that state. For the time you were a resident of CT, and are taxed by NY for the Unemployment, you would get a credit on your CT return for taxes paid to NY.
So you will need to complete your NY return first, then allocate the income accordingly to CT, with a portion of it being allocated to both state.
Ex. You received $10,000 in unemployment. You received $7,000 before moving and $3,000 after moving. Your NY return will include the full $10,000 while your CT will include $3,000.
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