It's there on his website. Or at least it used to be.
Since those were automatically published after a Certificate was established (based on whatever evidence, or lack thereof, the "state policies and procedures", as Chiyome Fukiyo would say, demanded at that time), one may surmise that the grandparents were the ones who filled in the form with the false information.
Except that if you read the birth notices they are all identically worded, and are obviously based on information provided by some government agency. And all the birth notices are on or about the same birth date as Obama. Which would mean that if Obama's grandparents fraudulently registered him for a COLB then it had to be done on the day he was born 8 or 10 timezones away. How would they do that and why the rush?