Typically a doctor can refuse to treat a patient all-things-being-equal. The problem is complicated if you're the only person in the area and you are working in a place that serves as the location's inpatient psych unit and there's no other places. Now there's something I got no idea on. As mentioned above I'd call the hospital's lawyer.
If there's another psychiatrist that also covers inpatient then the management could make the other doctor take that patient. Another thing you can do is consider filing for a restraining order and this would force the hospital to not make you work with the patient but you must have legitimate cause for such a request and you'd likely have to get your own lawyer for that one and not the hospital lawyer. (Wow this could be a landmark case! Only psychiatrist in the county has a restraining order against the patient, so the hospital can't the doc treat the patient but at the same time there's no one else to treat the patient!?!?!)
There's lots of things where training won't teach you what to do that I've encountered. E.g. A suicidal patient in my office, I call emergency services, and then the police arrive and refuse to take the patient even though the patient meets the legal requirements for the police to have to take the person. (Hey the police don't know the law in general, just like a lot of lawyers don't know a lot of the laws in general).
Or patient is seeing another doctor for a physical problem, and the other doctor clearly isn't doing their job, and the patient can't simply get another doctor, and you the psychiatrist know enough about the situation to know the other doctor isn't doing their job, but not enough to intervene and treat the physical problem.
Or police dump a patient into the ER that's clearly not mentally ill but say he's mentally ill to dump the patient onto you so they don't have to write up an arrest report.
