Do you have to have a statement from the doctor in order to exercise power of attorney over a dementia patient?

In general this is a: Two step process. First the doctor must do a capacity evaluation and then a court must agree that the patient is not competent to make the decision in question.

No: Power of attorney maybe given to someone themselves without an attorney being involved(just needs to be notarized). If the individual lacks the capacity to designate a proxy or won't if it is needed there may need to be a court process called a guardianship.