This from FactCheck.org:

The long form is drawn up by the hospital and includes additional information such as birth weight and parents' hometowns. The short form is printed by the state and draws from a database with fewer details. The Hawaii Department of Health's birth record request form does not give the option to request a photocopy of your long-form birth certificate, but their short form has enough information to be acceptable to the State Department.

To me, but then I'm not a birther, that says that the "short form" is the official document.