As the title suggest, I'm wondering something. Did Batman kill Doctor Death in Zero Year? When he and Dr Death fight on the blimp, things go rather badly for Batman and he's forced to set off a bomb. The bomb impales Dr Death with enough shrapnel to kill him.
Now here's the thing. Batman immediately believes Doctor Death can be saved, if only he recieves immediate medical attention. Dr Death declines this and instead asks Batman to tell the world the story of his son, who died overseas, subsequently, Dr Death dies. Now, do you think that Batman is directly responsible for Dr Death's... death or is it more indirect because he declined medical attention?
Funny side-note. Dr Death's supposedly dead son came back as red hood one, formed the red hood gang, then became the joker. His background as a soldier explains his combat ability, his knowledge with explosives and chemicals. You heard it here first folks!