The robots on Elysium cannot arrest a citizen. As stated by a robot at the end of the movie.
So who deals with criminals who happen to be citizens? Is the movie implying that the super rich are incapable of committing a crime? Surely the super rich are still super likely to do super stupid illegal things.
If there is a human police force onstation, will the robots allow a citizen to be detained? Or will they try defend them from 'harm', especially if the citizen resits arrest. How would the robot recognise a lawful backyard punch-up between neighbours to someone trying to avoid a lawful arrest?
What about a citizen onplanet. If they do something blatantly against the law, the robot will just stand by and watch? Probably even help out, to defend the citizen from the lowly mob?