Some fans believe that Batman has a "no killing" or a "no gun" rule. And some even think the Bat Cave is a "no peanut zone." But we know that Batman is pretty darn nutty, and that these rules were made to be broken. (Source)
In Tim Burton's Batman we see guns mounted on Batman's Batmobile and Batwing. We guess he thinks it's okay to shoot weapons if the car is doing it. Sure: blame the car.
However, we never see Batman himself wield a firearm. In fact, he gets shot a lot in this movie, and every time gets knocked down and almost knocked out. Batman needs some better Batbody Armor.
Instead, we see the mobsters, Joker, and his thugs using guns. The first standoff occurs between corrupt Lt. Eckhardt and Jack Napier. Later, Eckhardt orders his men to "shoot to kill" when pursuing Napier through Axis Chemicals. Finally, the Joker uses a gun with a barrel about as long as he is tall to shoot down Batman's Batwing.
Guns are definitely an issue in Gotham City, and Bruce Wayne would probably lobby for stricter gun control… with loophole for vehicle-mounted machine guns.