The means through which power and authority is shared in the criminal justice system is the same as it is shared in the civil area. The U.S. Constitution defines the scope of the federal government's power and specifies that all other areas of law, criminal or civil, fall under state authority. This means that crimes committed on federal land or actions which are illegal under federal law are matter over which the federal government has authority. Conversely, actions which occur in state lands or within a state's borders and that invovle only state criminal laws are matters states have full authority over.
However, there may be times when crimes violate both state and federal law in which both governments may compete for authority. In such cases it may be best to allow the government whose laws provide the strongest penalty, to help keep a criminal from the public longer and thereby protect the public better, to be the one to prosecute the crime. Once that sentence was provided it may also be possible for the other government to seek justice, similar to how states prosecute criminals who commit crimes in several states.
This process is how power is shared today and is effective in the overwhelming majority of cases. It would be impossible to develop a separate system that afforded equal power to both governments yet still assured the rights of each were supported.
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