No it doesn't. The robots in the movie have been programmed to protect and help the fellow police officers, and they follow their command, even if it is to shoot the criminals freely.
Chappie is shown to have a conscience along with AI, which makes him similar to human, and obviously humans don't follow the three rules of Robots as written by Isaac Asimov.
Chappie himself, once Deon uploaded the "Consciousness" A.I. program, does not obey the "Three Laws." In the film, Chappie appears to have free will.
The original police program for the Scouts does appear to obey Asimov's "Three Laws of Robotics." The machines obey human commands, and they appear to have self-preservation programming, as indicated by some of the dialogue in the film. However, the Scouts also appear to obey the "Zeroth Law", added by Asimov in "Robots and Empire":
"A robot may not harm humanity, or, by inaction, allow humanity to come to harm."
For this reason, a police droid in "Chappie" would be able to injure and kill criminals, as well as only obey humans who are authorized to issue orders to the droids, rather than all humans -- as this would ultimately protect humanity, or the population in general, according to their programming.