If you never lived in CT, you would report income earned from Connecticut sources as a Non-Resident. Although CT may tax this income, New York will give you a credit for tax you pay (or paid) to CT.
In your case, you could prepare your CT Non-Resident Return first, then MA Part-Year, then NY Part-Year. Here's more info on Allocating Income as a Part-Year Resident.
Take your time going through the State interviews. Although it may appear that two states are taxing your income, the end result should be that they are not. You may have to look at the final state tax forms to really see this, though.
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