Your employer is not correct. Your wages are taxed by both New York (because you work there) and Pennsylvania (because you live there).
PA will give you a credit for tax paid to NY but you have to (1) report your wages on your PA-40, (2) claim the credit on your PA return and (3) e-file a copy of NY IT-203 with the PA filing (TurboTax does this for you) to show that you filed a NY return and paid NY tax.
The NY tax rate is higher than PA so your PA state tax (after the credit) will be $0 for your tax liability but not $0 for the wage amount. If you have other PA income (investments, etc.) you may owe PA tax on those items.
Bethel Park
Does your W-2 list a local wage amount (Box 18). That is what you would use for Bethel Park. If the local lines (Boxes 18-20) are blank use the PA wage amount since that is your PA income.
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