I don't know if anyone here is familiar with it, but Tom Grant, a private-investigator hired by Courtney Love after Cobain's death, had found a great deal of contradictory evidence in lieu with Cobain having committed suicide. I don't think Courtney Love could have/would have killed Cobain, because even if she didn't have feelings for the man, she was, quite-frankly, riding his coat-tails to success and stardom. I know the Wikipedia article has a section for the "Suicide Dispute," it's a concise, but otherwise good read.

Kurt Cobain - Wikipedia, the free encyclopedia