The AI ends up recommending the patient commit suicide. Should YOU be charged with murder? It was your AI creation. A human therapist would likely be charged with manslaughter(murder basically) if they did something like that.
Would the human therapist actually get charged in that case however? It perhaps is unlikely the therapist can be charged criminally, unless you could prove that therapist undertook an act to advance that crime and aided them carrying it out - making them a cause or an accomplice. Generally your talks with a human therapist are confidential, and it's doubtful a professional would record anything so explicit.
It's not a general principle that if you do something illegal that your therapist can be guilty of something; even if you are following what you think their recommended course of action is.
I mean, even if they had said "I think you should go bust into the London gold vault and take all the gold".. That does not legally make them a cause for your actions if you choose to take that remark on your own and put it into action; it's not their action, unless they take an overt step forward, such as assisting you in planning your breakin, etc.
Merely talking about a crime or suggesting one does not cause or aid a crime in happening, etc. Even if you are seeing a therapist: you are expected to still know right from wrong. And if you don't, then you shouldn't be on the street, and what you really have in that case is a clinical malpractice violation.
So let me go back to that one...
The AI ends up recommending the patient commit suicide. Should YOU be charged with murder?
Should you be charged with murder. No.
Should you be found liable for a civil wrong: Yes. You are purporting to provide therapy, but it's a bogus product, and it possibly harms them further. If the patient ends up following that general recommendation.. I see how there could be an argument for wrongful death, but also it's tough to prove the causality, and that the liability should not be on the part of the patient who should have known the recommendation is wrong and inappropriate.