You will file a regular NY state form IT-201 as a NYC resident and a Connecticut non-resident form CT-1040NR. CT and NY have a reciprocity agreement where you get a full NY tax credit for income taxes paid to CT.
Your CT taxes should only be based on the amount of time you work in the state. For instance, if 80% of your time is spent in CT then 80% of your income is CT taxable income. Your employer should be accurately calculating and withholding the appropriate proportions.
However, NY taxes all income regardless of where it is sourced. Since CT has lower tax rates on income than NY and NYC, you should have income tax withheld for both states to avoid having a large tax liability in April. At the end of the day, you will effectively pay the equivalent of NY tax rates on all the income.
If you know they are over-withholding and you are looking to get back some of the money throughout the year instead of as a refund, you could alter your NY state withholding allowances with your HR department.