What is the representation of madness in Crime and Punishment?
Yes, indeed, Crime and Punishment is an excellent novel to use as the basis for a discussion of insanity. Raskolnikov's twisted notion that he is one of the "supermen" whose actions exist outside the law (http://www.enotes.com/crime/themes) lead him to commit murder. After his crimes, he descends further into madness as he suffers from guilt and obsession about what he has done. Another source I recommend, Doestovsky: The Author as Psycholanalyst by Louis Breger, which you can locate by using the google scholar search engine, you can read online. One chapter is devoted to the psychological aspects of this novel. I think you will find it very useful.
If we define insanity as being in a state wherein one has lost control of a normal ability to think and function, then we can say that this is a novel about insanity.
Raskolnikov loses his ability to maintain control of himself, acts impulsively, and at times seems to witness his own actions as opposed to choosing them. This is not to say that impulsiveness is equivalent to insanity. What I am suggesting is that Roskolnikov loses control of himself for extended periods.
This is a rather external definition of insanity, I think, but an argument can be made that insanity is best defined by outward manifestations of internal states.
I do agree that the novel can be read as a study of insanity, but to a certain degree. I think it is dangerous to think of Raskolnikov as fully mad at any point in the text because it perhaps provides him with some sort of easy justification for some of his behaviors. That said, his descent into a level of madness is arguably the "punishment" referred to in the title of the novel, rather than his jail time described in the Epilogue. His true punishment is his realization that he is not a "Superman" and his theory has failed. This realization does contribute to some madness on his part.
Raskolnikov suffers bouts of what might be called insanity, but he also has moments of great lucidity. He is often out of control, but at times he is in perfect control of himself. If guilt and delusions of greatness can cause insanity that comes and goes, Raskolnikov is a perfect example of insanity. If one chooses to believe he is simply a man who suffers from a horrible guilty conscience after committing a horrifying act, then he is not a good example of insanity.
The intellectual who feels himself superior to social mores, Raskolnikov commits what he believes is the perfect crime. However, he does not reckon on his conscience which leads him to a certain paranoia born of his guilt. This paranoia is, of course, not sane.