Sounds normal...there should be NY tax withholding showing on your paycheck...and on your eventual final W-2 form you get early next year.
When you live in one state and work in another....
1) ...at tax time you will first prepare a non-resident tax return for NY and calculate and pay taxes to the state you worked in (NY)...but just for the wages you earned in your work state...nothing else.
2) Then for your your home state (CT) , you prepare a resident tax return that calculates a tax on ALL your income from everywhere...wages, interest dividends, investments.......and once that is calculated, CT allows you to take a credit for the taxes you had to pay to NY for just the NY wages. (there is some math handwriting in that CT only allows a credit up-to what CT would have taxed those wages at....but that is all handled by the software).
When you do prepare your taxes next year...you need to first prepare every scrap of your Federal tax return first...the states won't be correct until every scrap of every income item and credits, and deductions has been entered in the Federal section first.....next the Non-resident NY tax return needs to be done....and finally the CT tax return. The NY tax return has to be done before CT because the CT tax return cannot determine the credit until the NY part has been completed.
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Folks living in the DC area, and some eastern midwest states, may work differently because the individual may work and live in "reciprocal tax states" where only the resident state gets all the tax, in spite of working cross-border.....but NY and CT are not reciprocal tax states, so the above discussion applies to you.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
