Obama's 'About the Issues'

The Democratic National Committee has a link on their site where people can ask questions about "the issues" - so I asked mine:

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Dear Sir/Madam,

As you know both John McCain and Barack Obama have had their eligibility for office questioned during this election cycle.

My question is this: What is the process for checking a presidential candidate's qualifications? Who is responsible for doing this? When is it done? What evidence is provided by the candidate that establishes eligibility? Clearly, some process took place - otherwise, it would impossible to certify these candidates as eligible, would it not?
I am most grateful for your time and attention, and eagerly look forward to your response.

Sincerely, Your Fellow Citizen, Justin W. Riggs