Angel Heart - Hrmm... the killing only lasts the first few chapters, but its an excellent psych manga, although not listed as such.
MPD Psycho - Now this is the one I am REALLY surprised no one listed. It fits your description perfectly.
SkyHigh - Nothing like that crappy movie of the same name, its really good, and almost meets your description.
Edit- ALSO
Parasyte - Really good. Not really about serial killers, but there are a lot of serial killings in it. Although, it is really a supernatural manga, so you may not like it.
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Does the walker choose the path, or the path the walker?