You should not have NY tax withheld if you are actually working in CT. Some businesses have an option where you can elect to have tax withheld for your residence state, but this is not common.
In most cases you will have a refund from your work state and a balance due with your residence state. This will depend on total income in CT and tax withheld as well as your exemptions, etc. Generally if you use single filing status and no more than 1 exemption on your state w-4 you should be entitled to a small refund from CT.