Out of State Student State Income Tax

If you are a New York resident, you pay New York tax on all your income no matter where earned, however I would also believe that you would owe Pennsylvania tax on that income if it was earned in Pennsylvania. 

You could ask the payroll department why local tax was  withheld, but not PA state tax. 

If the income IS taxable for PA, you would file a PA return, then NY. The tax you pay to PA will be credited on the NY return so that you are not double taxed on the same income. 

There may be something I'm not aware of concerning the income to make it tax-free, but just because state tax wasn't withheld does not mean it is tax exempt. 

NY link 

PA link