We know that the Batman doesn't kill, but in order to be effective, the criminal element of the city must believe that he will kill, and has killed. Criminals are violent and nasty people who have to be intimidated and roughed up to be subdued. Therefore, if criminals believe that Batman won't do anything more than push them around a bit, act scary and tie them up for the police, they would be more apt to use more energy and force to get away. Some readers might disagree and say that even if his adversaries know Batman does not kill, they will still be afraid of him because of the damage he could do to them and their business. I disagree. Batman must wield the ultimate fear over criminals. The fear of slow, painful death.
Due to the possibility of crooked cops, the general belief in the police force would have to be that Batman is capable of killing. Of course, since there cannot be a body (Batman doesn't kill), there really can't be an investigation. There would be times where someone was killed and the evidence pointed to the Batman. This has happened in the current continuity, but it isn't played up very much after the story has run its course. Commissioner Gordon knows that he can count on the fact that regardless of the circumstances, the Batman will not kill. Maybe this is why the police have stayed in check in regard to tracking down this "killer" vigilante. The Batman of the 1970s worked very closely with the police. How is that for a change from the killer night stalker of the 1940s?
All of the masked people who have closely worked with Batman have each been touched in a unique way by Batman's methods. Batman has had three protege's. The first Robin, Dick Grayson, "Laughing Boy-Daredevil," was trained by Batman during his early years. If we stay within the current continuity's history, we see that the major influences in Dick's training was the terrible impression left by the murder of his parents and Bruce Wayne's aversion to guns. Bruce had not yet fully developed his skills at intimidation, therefore this first Robin remained upbeat. The second Robin, Jason Todd will be discussed in more detail later, but suffice it to say that he most of all absorbed the Batman's training. The third and current Robin, Tim Drake, has seen Batman at his lowest and most dangerous in respect to his outlook as a vigilante. Tim's outside view of the Batman lead him to follow-up and support the no-kill philosophy fostered by Batman. Bruce has opened up to Tim relatively earlier in their relationship than he did Dick. In fact Bruce began opening up to Tim before Dick, and he never opened up to Jason. With Tim's high intelligence and his developed maturity, he has been able to maintain an objective outlook on the whole vigilante business. He views intimidation merely as a tool to be used against his adversaries.
This leads us to Jason Todd, the second and most tragic Robin. Batman readers know that Jason's life was cut short by the Joker. There are many reasons why the writers killed Jason, among them being the readers didn't really like him very much. This dislike grew from the fact that Jason wasn't the cooperative, jolly sidekick that Dick had been. Whereas Dick represented Bruce's good-natured child before his parents were gunned down, Jason was more like Bruce after the murder of his parents. Aside from being reckless and not following Batman's orders, Jason was suspected by many readers of killing someone. On purpose no less! This action goes against the very core of Batman's existence. The criminals can believe that the Dark Knight can and does kill people, but and readers must completely believe that Batman and his partners are incapable of killing. A dark cloud of suspicion hung over Jason after his run-in with a foreign ambassador's son by the name of Felipe Garzanos. Felipe was found guilty of attacking a woman, but due to his immunity from the local law, he walked away scott free (not the guy married to Big Barda). What was worse, he flaunted his obvious guilt, and continued to terrorize the poor woman. Enter Batman and Robin (well first Robin, then Batman), to put a stop to the mess. It is at this point that the facts become speculation. The only thing that the readers know for sure is that for some reason Felipe departed his apartment through the balcony. And as the Joker so eloquently stated, "It isn't the fall that kills you. It's the sudden stop!" Felipe Garzanos was dead, and Jason was the only other person in the room when he made his exit. When asked by Batman about what had happened, all Jason would say was, "I guess I spooked him." There are a number of things that could have happened in that apartment. First, Felipe could have had an accident and slipped, with no influencing factors by Robin. Second, Robin could have physically thrown Felipe off the balcony. Third, Robin could have attacked Felipe, and in that attack inadvertently knocked him off the balcony. Fourth, Robin could have intimidated Felipe so much that he either in a panicked state slipped off the balcony, or attempted to escaped from the "murderous" Robin and inadvertently fell to his death. The first alternative isn't likely because of Robin's reply to Batman's inquisition. We know that Jason had something to do with Felipe's death. The second alternative could have happened, but that would have taken a cold-blooded person to carry it out. This isn't likely because while Jason was a hothead, he was not a cold-blooded killer. The third alternative is a more likely possibility. While in a fight, Robin could have hit Felipe so hard that he knocked him off the balcony. While possible, it isn't probable since there probably would have been "words" between them prior to the fight. How much time would that have taken, and would the two of them be in the position for Robin to hit Felipe in such a way that he fell off the balcony. The fourth is the most likely alternative. Enter Robin with "kill" in his eyes (from his in-depth and effective training by Batman). Felipe can see that Robin will take no quarter, thus begins to panic. As Robin moves through the apartment Felipe retreats to the balcony. Robin closes in Felipe loses all sense and tumbles off the balcony. One might think that Jason absorbed the intimidation portion of Batman's training better than either Dick or Tim. We can only assume that Jason also knew the rule of no killing was paramount to everything, but he may have thought that if a scum-ball tumbles off the balcony of his own accord, the world will be a better place for it.
One more aspect of Batman's intimidation can be explored in Jean Paul Valley's short, disastrous stint as the Batman. Jean Paul pushed the intimidation and violent aspect more than what was acceptable by the readers and Batman. In fact, Jean Paul's allowance of Abattoir's death might be equated to actively killing him. While Bruce was visibly shaken by Jean Paul's ruthless method's, one must admit that it sure didn't hurt Batman's reputation with the criminal element, and Bruce didn't even have to do anything to achieve it.
If you want to be known as one of the big dogs, you have to do some things to make people think you will bite. The dog with a reputation of tearing someone's throat out will keep more people out of the junk yard than the toothless hound that just bays at the moon.