In answer to the OP, I would agree with pba that we can’t know. I just want to point out that there are two elements to the bechirah. Even if he may have been incapable of choosing to not commit his horrible crime, he may have been, at some point, capable of seeking help, yet didn’t.
Re: bombmaniac’s post, I think there’s a logical flaw. To assume that a crime was caused by mental illness is not the same as assuming that mentally ill people tend to be criminals.