Asimov's I, Robot isn't a novel, it's a collection of short stories about the evolution of positronic brained robots and the 3 Laws of robotics. It's been a long time since I've read it, so I don't remember the details of the individual stories. From what I've seen of the trailer, the movie seems to closely resemble the plot of Caves of Steel (an actual novel), in which a robot is accused of murder (theroretically impossible under the 3 laws) and the crime is investigated by a robot-hating human detective. Two later robot novels, The Naked Sun and Robots of Dawn are also 3 Law-based murder mysteries.
There may have been a murder-mystery story in I, Robot -- I don't remember it well enough, and my copy is 2000 miles away -- but the story titled "Evidence" may be the source.
FYI, the 3 laws are:
1) A robot may not injure a human being or, through inaction, allow a human being to come to harm
2) A robot must obey orders givein to it by human beings except where such orders would conflict with the First Law.
3) A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.
Good code for Paladin Warforged of Eberron?