I'm sure he did it to himself. He's always flirted with the idea of suicide, and had several close calls over the years preceding his death. Plus, he escaped from rehab within several days of his death, so he was more than likely on a bender. He purchased his gun he shot himself with as well not long after escaping, and Courtney was out of the state all that time, so it would be really unlikely that she had anything to do with it, considering he bought his own weapon.
I watched the documentary Kurt and Courtney thinking it might shed some new light or offer new information I hadn't seen before, but it seemed like 1 1/2 hours of wishful thinking, rather than gripping evidence. Kinda like with Elvis and Tupac fans, people just dont want to believe they're really gone, or that they were actually that fucked up that they would allow themselves to be part of a lifestyle with a tragic end result.
Kurt was a sad sad man with serious emotional problems. It's hard to accept that anyone could take their own life, but from everything I know about him, from everything I have read and researched... thats the conclusion I find to be most likely, as sad as it is.