"The murderer shall not die until he stands before the congregation in judgment"—Numbers 35:12.
It is forbidden to execute a criminal guilty of committing a capital crime before he receives due process before a rabbinical court. (This prohibition applies after the crime was committed. With regard to a criminal in the process of executing a crime, see Negative Commandment 293.)
Even if the members of the High Court witness the execution of a capital offense, they must serve as witnesses (before another panel of judges) who will adjudicate the case.