This is who the killer is and details to help you understand.
First of all notice when the detective shows up when molly looks out the window, no one has been killed yet and notice he has a glove on one hand and not the other. After the first murder the detective shows up again, this time he talks to molly still we see one hand with a glove and the other no glove. Molly then goes to the murder scene and finds the detective, and listen to how he describes her screaming and so on. Also, again we see one hand with a glove and the other no glove.
Ok still with me.
Now remember after the 2nd murder of the stupid blond and the class scene and all when the professor is going to his car and is startled by the detective. Remember how the detective said he didn't believe molly's theory, well he said "maybe no motive at all" and laughs. Also notice that when he asks if he can keep the professors book you see once again the one hand holding the book has no glove, and the other hand does. Remember when molly stabbed the guy on the boat in his left hand. Notice how the detective has that exact knife from the boat. Ah following me on this one. He was also the lead on the case and now he is again the lead detective. Also do you notice the detective always has a butcher knife on him even at the professors home.
Notice when they are at the professors home when molly sees the necklace and then is startled by the professor, well the prof sees the necklace and picks it up and goes after molly. Then as the professors is knocked out by the detective he pulls the necklace out of the professors hand. The detective can keep any evidence he likes if nobody knows, plus he has access to blood samples and the morgue ah still with me.
The professor is really executed, that is not molly's dream, cause his voice is the dub not hers. The professor gets the death penalty for the murders exactly what the detective had planned. As for molly, she went insane at the end thinking she was the killer but she isn't.
When something really bad happens to you twice it will make most people go insane. That's the answer and to clear all the dumb theories I've read on here. Remember you have to be observant when it comes to movies like this otherwise people think it's stupid because it's beyond their understanding.
People who want everything layed out on the table in a movie obviously don't read books which require thinking and an imagination.