There seems to be some misunderstanding here. Federal prosecutions are tried before the federal district court, which has its courtroom in the federal courthouse. If there is such a thing as a state district court in your state (some states have a "distict court," others don't), that is a different court entirely.
In NC, there are two different types of "District Court." The first is state district court, which is basically traffic/misdemeanor court for state criminal charges. The second is federal district court, which is the trial-level court for all federal criminal charges. If you are charged with a federal crime, you will be tried in federal district court, which is located in a federal courthouse. There are federal district courthouses in many towns in the eastern part of the state, including Raleigh, New Bern, Greenville, Wilmington, and Elizabeth City.
Federal criminal charges are very serious, and being in federal district court is much different than being in state district court. If you (or a family member/friend/etc) have been charged with a federal crime, you should contact a local defense attorney here in Raleigh immediately. Feel free to call me at 919-838-0058 to discuss the case, or you can read more about federal prosecutions on my website at http://www.halecriminallaw.com/criminal-defense/federal-crimes.
There are two district courts in North Carolina: the state district court and the federal district court.
If you are charge with a federal crime you would be tried in the federal district court. You can be charged with a federal crime and a state crime based on the same conduct, so you could be tried in both state and federal court for the same conduct, but you would have a state warrant or indictment if you had a state case.