From the first page of that document, not shown above, it is important to note these words:
“I am a natural born citizen of the United States, am at least thirty-five years of age, and have been a resident within the United States for at least fourteen years.”
Found it:
http://www.thepostemail.com/wp-content/uploads/2010/10/Arizona-BHO-Notarized-Statement-page-1.jpg
16-351. Limitations on appeals of validity of nomination petitions; disqualification of candidate
B. Any elector may challenge a candidate for any reason relating to qualifications for the office sought as prescribed by law, including age, residency or professional requirements, if applicable.
Of course, there may be a law in Arizona against knowingly providing or signing to false information or false statements on a nomination form. General election penalties range from both misdemeanors and felonies. If that form was submitted in Sheriff Joe's jurisdiction, then perhaps he can take action against Obama for election fraud.