The handling of criminal matters within the military happens inside the military. For minor crimes, commanding officers will usually handle investigations and make decisions about what happens next.
They will typically work with attorneys on the matter but hold the ultimate say in what will happen. The commander may make a few different choices regarding what to do next.
The commander may decide the offense is serious and needs to go before the court. In this case, he or she would move the charges to a court-martial. This is similar to going to civilian court when charged with a criminal matter. There will be a trial and evidence presented.
The commander may feel the situation does not warrant any further action. After looking into the matter, he or she may find the claims are untrue or feel the situation was minor enough that having the investigation was punishment enough to teach a lesson.
The commander may hold an informal hearing about the matter. This is a small event that provides the commander with the duties of a judge. He or she will decide the punishment and what happens moving forward. A hearing does not involve evidence and witnesses. It is far less complex than a court-martial.
The commander may also take administrative action to correct the behavior. This is in opposition to punishing the person for the alleged crime. It is serious but will not result in further criminal actions.
The right to handle minor criminal matters is very serious for commanders. They hold a lot of power over what may happen in the end.