Employees live in PA but work in NY state should PA taxes be withheld?

I have a small business with a couple employees. These employees with myself included live in Pennsylvania but work in New York state. Should my business be withholding PA taxes? My business already withholds NY taxes. TIA

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Since PA will grant its residents a credit for the taxes paid to New York on income taxed by both states, and since NY's income tax rate is considerably higher than PA's, it is probably not necessary to withhold PA taxes.

**Answers are correct to the best of my ability but do not constitute tax or legal advice.