I maintain NC residency but work in DC. I am filing DC non-resident, do I report the tax on my wages to NC? I have to file NC taxes to maintain residency.

I maintain my permanent residency as NC. However NC is fine and dandy with you living out of state so long as you pay them taxes. My employer will only take out taxes for the states in which it operates (DC, MD, VA) so I was instructed to have DC taxes taken out during the year and then file for DC-non resident, in order to recoup my money and pay my state of residency their due tax. My question is when filing do I note that another state has already taxed my wages or is that null and void because I'm going to file DC-non resident? I just want to make sure that I am paying the proper amount of taxes to NC.