The Arizona Senate has passed a bill which, if passed by the House and signed by the governor, would likely guarantee that President Obama would not be on the ballot in that state. As Dave Weigel notes:
A CERTIFIED COPY OF THE PRESIDENTIAL CANDIDATE’S LONG FORM BIRTH CERTIFICATE THAT INCLUDES AT LEAST THE DATE AND PLACE OF BIRTH, THE NAMES OF THE CANDIDATE’S MOTHER AND FATHER, INCLUDING INFORMATION SUFFICIENT TO DETERMINE THE CITIZENSHIP OF BOTH PARENTS, THE NAMES OF THE HOSPITAL AND THE ATTENDING PHYSICIAN, IF APPLICABLE, AND SIGNATURES OF ANY WITNESSES IN ATTENDANCE.
That’s for every candidate, so only Donald Trump can qualify for the ballot as of right now. This has been written so that Barack Obama’s certificate of live birth, which does not include the name of the hospital and attending physician, does not count.
It is actually the Certification of Live Birth that was released. The longer-form Certificate of Live Birth from Hawaii is not permitted by law to be released.