In parashath Shofetim [Deuteronomy 16:18-21:9], we learned that we were to take any case- which was too wonderful for the local magistrates- to the place YHWH chose to set His name- to the Kohanim and Judges presiding in those days and in that place [Deuteronomy 17:8-13].
In parashath Khi Theitzei [Deuteronomy 21:10-25:19], we are given the example of a case concerning a son who will not obey his parents- even after they have corrected him. In this case, the parents were told to seize the child and take him to the gates of his city and to the elders of his city and explain the case. The child is then stoned to death [Deuteronomy 21:18-21].
Here is a clear case which was investigated and the accused was clearly guilty; the child was not taken to the Place and to the Kohanim and Judges, but to his own city and to his own elders. The people of his city would have been familiar with the case and knew that the parents were speaking truthfully and the child- indeed- was stubborn and rebellious.
In last parashath Shofetim, we were given the example of an accidental death; the one which killed his neighbor had the opportunity to flee to the city of refuge [Deuteronomy 19:4-13]. In the city of refuge, he was afforded the right to trial and present his case. The Kohanim were to take the man to that Place and to the Kohanim and Judges in those days who were to diligently examine the case. If found guilty, the man was delivered to the redeemer of blood for execution. If found not guilty, he was remanded to the custody of the city of refuge until the death of the Kohen Gadhol [Numbers 35:25, 28].
In this last case, the accused was taken to the High Court and tried. This is because, in the case of accidental murder, there would be no partiality due to familial relations in the city in which the accused and his neighbor might have lived. He would be given a fair trial.