It depends. You should only have NY tax withheld if you either live in New York (working in KY), or are working in New York. While NY does tax a telecommuter who works from home on behalf of a NY company, this doesn't sound like your situation because you state the company is in KY. So, if you had NY taxes taken out, these are the possibilities:
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If you live in NY, you will file a KY nonresident return, and a NY resident return. Both states tax you, but NY will give you a credit for the tax you pay to KY on the income you earn there. You may not get back all of the NY withholdings, but you should get a good portion of them back.
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If you only work in NY, you file a NY nonresident return, and NY determines the tax on your NY income. Your tax withheld is compared with your tax liability, and your refund (or the amount you must pay) will be the difference between what you had withheld and what is the tax liability.
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If you neither live nor work in NY, the taxes withheld were in error. You would file a NY nonresident return and allocate that you had zero income in NY. New York will not allow you to e-file this type of return, so you will have to mail in the return (and ignore any diagnostics that say that NY requires you to e-file. They won't let you e-file this return).
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