My employer took out some local NYC taxes but I am not a resident. They told me to request a credit on my taxes. How do I do that?

You will need to file a nonresident income tax return for New York.  Form IT-203 will then be generated and you will be able to claim a refund for your income taxes paid in.

To ensure your return is calculated correctly, you will need to confirm a few items: 

In the My Info section of TurboTax, confirm that you have entered the correct state information: 

1. Click Edit to the right of your name 
2. Confirm your input under #2 Tell us the state(s) you lived in
3. Go back to the personal information section, and verify the mailing address and "Other state income" section.  Be sure to answer yes or no as applicable to the question asking "Did you make money in any other states?". 
4. Review your input in the Federal section under Wages.  Ensure you have only reported the New York City wages and withholdings are reported on your W-2 Form.

Please note the following as it will affect the calculations: 

When you are preparing more than one state return, make sure you prepare the nonresident year resident New York state tax returns first.   Be sure to answer the questions correctly to ensure only income sourced to that state specifically are reported.  If there is no income that is sourced to New York state, please indicate the source of the income.

Assuming none of the income is sourced to New York City, your return should reflect the overpayment and refund the excess withholdings.