It depends.
Typically you are taxed on income in your resident state, or in your case, Connecticut. This is assuming you will be returning to CT after completing your education in New York.
Absences from a state to attend school in another state is considered a temporary absence and not a change of domicile unless you have intent to move to the other state.
New York would tax you on any income earned within New York and you would be able to claim a credit for taxes paid to another state on your Connecticut return.
We would not be able to verify how much your taxes should have been here. However, I have attached a link to the New York Nonresident form instructions with the tax tables starting on page 55.
You can use the information based upon your tax return to determine what your tax liability should have been as compared to what was reported on your tax return as filed.
New York nonresident form instructions
If you determine your New York return was not prepared correctly, you can prepare an amended state return to make the corrections.
The following link can be used to assist you with preparing the amended returns using TurboTax.
Steps for amending state returns in TurboTax
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