My best GUESS is that, in the end, the perpetrator may turn out to be someone we don't "know" or haven't paid much attention to. IF polygraphs were failed, could it be because the one(s) being administered the polygraphs felt pretty sure they knew who committed the crime and somehow felt responsible for the circumstances that caused the perp and MC to cross paths and know one another, if they did? At least some of the questions might be failed that way....?
I further GUESS that the motive for the crime could be a feeling of being spurned, which could be pure invention in the mind of a very, very disturbed individual who never would have seriously been in the running for MC's affections in the first place. I wouldn't think that rape would necessarily have to be a part of that scenario but I haven't studied the statistics.
The perp may or may not be a person who ends up being a serial killer, if they aren't already. The varied methods used in cause of death might well indicate a first victim, with desperation and inexperience being manifested. (Conjecture.) Whether the person goes on to murder again could depend upon many factors. For now, the "venting" has occurred. If similar spurning is perceived by the disturbed mind, the perp now has past horrible but "effective" actions in his "bag of tricks". It is often easier for we humans to repeat an action we already know than to create a new response to "problem-solving". All pure imaginings of mine.
