As an employee - you may withhold income tax
based on residency of your employees. That is based on requests of employees. Generally - you are not obligated to do so.
But you are generally required to withhold income taxes based on the place of employment.
When you issue W2 form - you will income as taxable for the state where the work place is located, but if there is no withholding - that would be zero.
As a practical matter if the employee will file that state tax return and pay the tax liability calculated on that return - penalties are unlikely.
However - if the employee would fail to do so - the employer might be held liable for failure to withhold.
For instance for NJ - see page 12 - http://www.state.nj.us/treasury/taxation/pdf/current/njwt.pdf
Failure to file a report by the due date
and/or failure to remit any taxes due by the due date will result in penalty and interest charges. Anyone required to withhold gross income tax does so as a trustee on behalf of the State of New Jersey. Thus business owners, partners, corporate officers, and some employees of such businesses may be held personally liable for failure to collect the tax when required or for failure to file returns and remit any taxes due on a timely basis.
Late Filing Penalties - 5% per month (or fraction thereof) of the balance of tax liability due at original return due date not to exceed 25% of such tax liability. A penalty of $100 per month (or fraction thereof) for each month return is delinquent may also be imposed.
Late Payment Penalty - 5% of the balance of the taxes due and paid late.
Interest - The annual interest rate is 3% above the average predominant prime rate. Interest is imposed each month (or fraction thereof) on the unpaid balance of the tax from the original due date to the date of payment. At the end of each calendar year any tax, penalties, and interest remaining due will become part of the balance on which interest is charged.