We reside in Texas, that is where we have our home and an address. My husband is a consultant and at this time works in North Carolina. The company he is working for is withholding NC states taxes. Is this correct. He lives in a hotel and does not have an address in NC. Should we pay taxes where we live or where we work. If it is OK to withhold NC TAXES can we claim later because we are non resident, it is a 6 month contract.
Thanks

If he works in NC, then he owes NC income tax on the money he earns while working there. He should file a non-resident tax return with NC.

You pay taxes first to the state you work and then to the state you live in. Of course as a TX resident you don't have to worry about the latter.