It depends where the district court is. Many states have courts that they call "district courts" but what a district court is responsible for varies state to state. Fortunately, many courts now have website where you can look up information about the court, including what kind of cases it handles.
U.S. District Courts
district courts are responsible for determining the facts of a case. They take both criminal and civil cases. In a criminal case, a district court will decide if a person is guilty or innocent based on the evidence presented.
Local courts and district courts.
Courts that have the authority to be the first courts in which most federal cases are heard are known as district courts. These are the trial courts of the federal judiciary system and are responsible for hearing both civil and criminal cases.
Federal district courts have jurisdiction over trials. Federal appeals courts have jurisdiction over appeals from the federal district courts.
Federal district courts have jurisdiction over trials. Federal appeals courts have jurisdiction over appeals from the federal district courts.
The US District Courts (trial courts), because they handle the majority of federal cases.
The district courts in U.S. territories are generally referred to as "District Courts." For example, the District Court of the Virgin Islands and the District Court for the Northern Mariana Islands. These courts have jurisdiction over federal cases in their respective territories, similar to U.S. District Courts in the states.
Federal district courts have jurisdiction over trials. Federal appeals courts have jurisdiction over appeals from the federal district courts.
Federal district courts have jurisdiction over trials. Federal appeals courts have jurisdiction over appeals from the federal district courts.
Federal district court.