***Possible spoilers for issues of Detective Comics (featuring the Batman) from the late 1930s.***
Thanks to the Comixology Batman sale, I ended up getting a few of the early issues of Detective Comics and Batman for 99 cents. I've read the Detective Comics right after the infamous #27 that introduced Batman and learned a couple things:
1) Either they didn't dust for prints back then, or Batman was so confident no one would believe for a minute that lazy (tobacco) pipe smoking playboy Bruce Wayne could be the vigilante that he didn't care enough to bother wearing gloves. As you can see on the cover for issue 29, no gloves.
2) There have been images from early Batman's early adventures showing that he used a gun, but that wasn't the only way he killed people. This was more of a surprise to read than the no gloves thing, which could have just been an issue of coloring, and was corrected in the next couple issues.
In this first set of panels, he kills someone by tossing them off the roof of a tall building. Notice also the lack of gloves.
Later on, he swings in on his rope in order to break a bad guy's neck! And the dialog shows it was no accident.
And not only does the Batman kill, along with training in boxing and jujitsu, he also passes along the skill of tossing bad guys to their death to Robin, who tosses his first bad guy to his death in this panel.
Obviously, at some point Batman was characterized as having a "no kill" rule, and being very anti-gun, but before that, Gotham's prisons probably weren't as filled up as they are today.