I have one character with double digit assault numbers on record, but only 1 brawl and no murders. Another character has double digits for assaults, 2 brawls, and almost 10 murders.
To the best of my knowledge as the person behind the keyboard there has only been one instance that might even remotely qualify as murder and that was the stupid Whiterun Guard that wanted the glory of the killing stroke on a dragon and who jumped in between the arrowhead and the dragon at the moment the arrow was fired and took it in the back at a distance of about 3 - 4 feet. That same character has found another dead Whiterun Guard who might have met with the same fate from a much longer distance but I don't know for sure what killed that guard.
But aside from some Stormcloaks of whom he killed 3 he has only killed bandits, undead, and wildlife such as skeevers, wolves of various types, and a few elk. No chickens, cows, etc.
So just what causes you to get counts in the Crimes Section for murder and assault, and even more importantly get a bounty awarded for a character?