Hi there!
You have raised a valid point. I cannot say much for psychiatrists. But I am a psychologist and psychotherapist so I can speak for my professional community. Yes, we do have such a form being signed by both parties, i.e. the client as well as the therapist. Usually, this copy is retained by the professional as part of their paperwork but a copy of it can be given to the client as well.
Next Steps
Discuss your concerns openly with the professional who is treating you.