Hi Noemi,
I am not sure if there is a law to be required for the doctor to do so for dementia. It is not like seizure for younger people and sometimes requires the doctor to write something to prevent the patient from driving. (Seizure in the case of Alzheimer's is in very late stage and does not matter.)
However, it is very common that the family needs to ask the doctor to write a letter about the disease and staging indicating that the patient is incompetent. This way, the family can process lots of legal paperwork with the letter. Otherwise, the doctor is not required to do anything. It is pretty much up to the family or the patient to ask for a letter indicating the diagnosis.
Hope this helps,
Nina
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