State tax filing

I need to edit my response, after I went back and read @Vanessa A message. 

She was correct in saying that because you worked no days in NY, you're employer was correct in only withholding taxes in your home state.

She was incorrect in saying that most people meet the Convenience of the Employer test, most do not. The reason you are not subject to tax in New York, is because if you worked 0 days in New York, and are not subject to the convenience rule. If you were, you would likely fail it (>95% + of taxpayers I represent would fail it). 

Here are the 2009 employer Withholding Guidelines issued by NYS, that contain language on Page 41, that allow them to not withhold if you work no days in NY:

Employees who expect to perform no services in New York may submit, but are not

required to submit, an IT-2104.1 to their employer estimating a percentage of services

performed in New York of 0%. The employer may rely on the IT-2104.1 as long as the

employer does not have actual knowledge or reason to know that the Form IT-2104.1 is

or has become incorrect or unreliable.

Your employer is one of few actually doing the right thing, kudos to them.