system
Given the following post, respond as if you're commenting on Reddit:
human
[Warhammer 40k] How would a commanding Sister of battle eg: Sister superior, Cannoness react to a Commisar executing a battle sister for perceived cowardice/heresy?

Also what are the rules regarding cross faction jurisdiction? Can an inquisistor order a space marine? A guardsmen general order a mechanicus unit and so on?
gpt
A Commissar who *blam*s a Sister better start explaining himself pretty quick, or else they're going to get flamethrowered.

The Commissariat is a component of the Astra Militarium, a *whole different branch* of the armed fighting forces of the Imperium. They have *zero* intrinsic jurisdiction over the members of the other groups; the Sisters are in charge of their own discipline, and if anything their treatment of perceived cowards is even more brutal than a Commissar. For them, a laspistol to the back of the head isn't punishment, it's undeserved mercy. 

As far as overall jurisdiction in joint situations, the word of the day is "political clusterfuck". Imagine the worst territorial bickering between the Air Force, Army and Navy, or between federal law enforcement and the local boys, crank it up to 11, and give some of the participants authority to commit mass murder without a permit.