Where you "reside" is only part of the story. It matters where you physically work. Do you work at the client location in North Carolina, even only occasionally, or do you work exclusively in Virginia?
Any income you earn for working in NC is subject to tax by NC. Since you live in VA, all of your income is subject to tax by VA, no matter where the income is from. If some or all of your income is subject to tax by both states, you will get a credit on your VA resident tax return for part or all of any tax that you pay to NC.
However, if you work only in VA your income is not subject to NC tax, and you do not have to pay any NC tax. It doesn't matter where the client is located. If you physically work only in VA, your employer should not be withholding NC tax. If you never work in NC, and they are withholding NC tax, they are just doing it wrong. You should just ask the payroll department to stop withholding tax for a state that you don't work in. If they want you to fill out a form for that, ask them to give you the form.
Did you previously live in NC? If so, that could be why they are still mistakenly withholding NC tax. Did you properly notify payroll that you moved?
