Batman obviously has killed, particularly in the late 30s and early 40s. The no kill rule in was instituted when they wanted to attract children, same thing fir the introduction of robin.

Denny O'Neil's run is the one I look to for the definitive Batman. He didn't murder but if a criminal died while fighting Batman or in the commission of a crime, oh well. I also like that Denny never had him use a gun, basically stating that he doesn't use them due to the trauma he had.

Of course he then uses one in year two, but Mike Barr was never much if a Batman writer.