Breakin' the Law
Jurisdictions
Canon Law
All clerics were covered by canon law, not civil law. The Church had its own courts, lawyers and legal traditions. This was one of the chief privileges of being in the clergy and was a privilege fiercely defended at every level of the Church hierarchy.
The "criminous cleric" caused much controversy in the late Middle Ages. That is, when a clergyman committed a secular offense, such as robbery or assault, he was tried by the Church, not by the State. Kings quite naturally didn't much like this system and tried every trick in the legal book to have clergy tried in their own royal, or at least baronial, courts. Likewise, the Church expended much effort to ensure this did not happen.
Sometimes the Church tried and condemned, but then turned the criminal over to the State for punishment, especially in the case of executions, but also for minor stuff that might require a whipping or branding or the stocks. More often, though, the Church imposed some sort of penance, which might be very minor.