If you are looking only at the federal court system, a person can only be tried for capital murder in a federal district court. If a person's case is appealed (either by the defence or by the prosecution) that appeal could be heard in appellate courts, but the actual murder trial would not be held in those courts.
In the federal court system, only the district courts hear actual criminal trials. If a person were to commit a federal crime that carries the death penalty, they would be tried in such a court. For example, Timothy McVeigh was tried in a federal district court for carrying out the Oklahoma City bombing that killed 168 people in 1995.
Please remember that most capital murder cases are state cases. They are not tried in the federal court system at all.