Story highlights Support for mental and physical exams similar to 2004

Public divided on whether a president has the right to keep health records private

Younger Americans, women more supportive of required mental exams for presidents

Washington (CNN) Americans continue to broadly support annual checkups for their commander in chief, according to a new CNN poll conducted by SSRS, but they are divided about how much information about his or her health a president ought to make public.

The poll finds that 82% feel a president should be required to take an annual physical examination to check the condition of his physical health. Only slightly fewer, 77%, say a president should be required to take an annual exam to check for mental conditions, such as Alzheimer's Disease or depression.

The broad support for required checkups are perhaps not surprising in light of another finding in the poll: 90% say a president's health is important to his ability to do the job well, including 64% who consider it "very important."

Support for both physical and mental exams for the president are about the same as they were in polling conducted during the 2004 presidential campaign, when 84% favored annual physical exams and 79% backed annual mental checkups.

But public opinion has shifted away from presidential privacy. In the 2004 survey, 61% felt that presidents should have "the same right as every other citizen to keep his medical records private," while 38% thought presidents "should publicly release all medical information that might affect his ability to serve his term as president."

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