When is the "insanity defense" applicable in Jewish Law?

Question

In regards to the Halimi murder in France, a person made the assertion that Jewish law would agree with the recent verdict, as someone judged to lack discernment is not culpable. My memory is that there are two categories applicable here: someone who is insane and mistakes a potted plant for Satan, for example, and throws the plant out the window wouldn't be culpable if the plant hit a passerby. In the real-world case, the murderer had threatened the victim prior to the murder and specifically targeted her, which speaks to maintaining some degree of discernment (i.e., he knew right from wrong and was deliberately choosing wrong.)