The way this works is that these states all work on your full income as adjusted for various state additions and subtractions and then they calculate a state tax.
Please do your CT and NJ state returns first, then do your NY return. This will give TurboTax the opportunity to calculate the taxes from the nonresident states and carry these amounts to line 41 on your IT-201, which is the "Resident Credit".
This credit is a dollar for dollar credit for taxes paid on the same income in other states. In this way states try to avoid double taxation of the same income (this works more or less well, depending on how close the states' tax rates are).
If you have already done your state returns, go to line 41 on the IT-201 and make sure that it is equal to the sum of the credits in the other two states. If no, run through all three state interviews again (CT, then NJ, then NY) to give TurboTax a chance to pick up the line 41 amount.
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