How should AI agents hand off to humans in healthcare?

I've been building an AI that handles WhatsApp conversations for independent medical and dental clinics — answering questions, quoting treatments, booking appointments, sending reminders.

The hardest design problem hasn't been the scheduling logic, it's been deciding exactly when the AI should stop and hand off to a human. Right now it escalates on anything sensitive or outside what the clinic configured, but I keep second-guessing where that line should sit in a trust-sensitive space like healthcare.

For anyone building agents in health, legal, or finance: how do you draw that line? Hard rules, confidence thresholds, or something else?

(Happy to share a quick demo in the comments if anyone's curious how it works in practice.)