Basically that is what happens. But there are subtleties. (NY will tax you only on money made in NY, CT will tax you on income you earn worldwide, but give you a credit for tax paid to other states).
You should do the NY non-resident return first because you need to know the amount you owe to NY for the CT credit. That might reduce your CT tax to zero, it might not depending upon the different state rates and deductions and the like.
Here is CT's article on this:
http://www.ct.gov/drs/cwp/view.asp?a=1462&q=266294
Your employer should probably be withholding taxes for NY (place of work) not CT (residence).
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"
