Since I live in NY and work in NJ should my payroll service be withholding state tax for NJ or NY?

Thanks

If you are present in a state, then any income earned during this period, must be reported to the state. So you must pay NJ taxes.

To your resident state, you must report your worldwide income for the year.
Read: Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

Since I live in NY and work in NJ should my payroll service be withholding state tax for NJ or NY?

Thanks

A little of both. First they should definitely be withholding NJ tax. But because NY's rates are generally higher than NJ's, depending on your income you may find that you still owe some to NY. So it may be wise to ask your employer to also withhold some amount for NY out of each paycheck so you don't have a big tax bill to NY at the end of the year.