Criminal Prosecution in Washington, DC

Because the District of Columbia isn’t a state all crimes are considered federal crimes, even when those laws are passed by the DC Council, and the US Attorney for the District of Columbia handles local prosecutions as well federal prosecutions as other US Attorneys. Federal crimes are tried in the US District Court for DC; local crimes (ie anything that would normally be handled under state law) are tried in the Superior Court of DC. What happens when someone is accused of both federal crimes and local crimes? Would they undergo two separate trials like defendants in states or single trial for both sets of crimes?