I'm Lucy, and I'd be happy to answer your questions today.
There is no law that would require a doctor to shred a letter from a family member about a patient without reading it (since they'd have to read it to know what it was). It would be a violation of HIPAA for them to respond to him and give him any information about you, your condition, or your treatment. If they do that, you could sue for a privacy violation, UNLESS your father is involved in providing care to you, or paying for your care and you do not object. It doesn't sound like that's your situation, but if it were, you'd be able to tell the doctor that you objected and he would have to stop sharing information with your father.
Take a look at this list of examples for types of situations where your doctor could talk to your father.
However, they also are not bound by the letter or the requests made in any way, and the letter carries zero medical weight. If you have a doctor who would put the wishes of the parent of an ADULT patient ahead of the patient, then it may be time to find a new doctor. And there is no logical or legal reason your father would need to know who that new doctor was.
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