If it was all received from New York based on New York income then all of it goes on the New York return.
Do the New York part-year resident return first. (If you did it out of order delete it and start over) Enter all New York source income there. Then do the Connecticut return. Connecticut will give you credit for any taxes paid to New York on any amount taxable to Connecticut. TurboTax will carry over the credit for you.
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