I gather that the only possible proof would be the Area Number, and the fact that the number (I assume 04X, like mine) is one associated with Connecticut. The underlying assumptions Taitz is making are that SSN are assigned at birth, and that the Area Number is intimately associated with the state in which you were born.
From the Social Security Administration's official site:
The Area Number is assigned by the
geographical region. Prior to 1972,
cards were issued in local Social
Security offices around the country
and the Area Number represented the
State in which the card was issued.
This did not necessarily have to be
the State where the applicant lived,
since a person could apply for their
card in any Social Security office.
Since 1972, when SSA began assigning
SSNs and issuing cards centrally from
Baltimore, the area number assigned
has been based on the ZIP code in the
mailing address provided on the
application for the original Social
Security card. The applicant's mailing
address does not have to be the same
as their place of residence. Thus, the
Area Number does not necessarily
represent the State of residence of
the applicant, either prior to 1972 or
Generally, numbers were assigned
beginning in the northeast and moving
westward. So people on the east coast
have the lowest numbers and those on
the west coast have the highest
Note: One should not make too much of
the "geographical code." It is not
meant to be any kind of useable
geographical information. The
numbering scheme was designed in 1936
(before computers) to make it easier
for SSA to store the applications in
our files in Baltimore since the files
were organized by regions as well as
alphabetically. It was really just a
bookkeeping device for our own
internal use and was never intended to
be anything more than that.
So depending on when President Obama got his SSN the area number could be based on either the office he was at when he applied for it or the return address on his application. Keeping in mind that in the past people didn't necessarily get a SSN until they actually needed it (usually when they got their first job or applied for the draft), there's a good chance that Obama applied for his sometime after 1972, and possibly during the time when he was at Columbia University in New York City. If that's the case a return address in Connecticut is hardly unlikely or suspicious.
Edited to debunk my own theory...
I've since found a website that has different explanation for how President Obama got a Connecticut number. Documents show Obama received his number in 1977 when he still living in Hawaii, not when he was at Columbia. However, according to The Fogbow:
So how did President Obama get a
Social Security number with an Area
Code reflecting residence (or mailing
address) in Connecticut?
Most likely, this was due to a
clerical error. At the time, President
Obama lived with his grandparents in
an address on Beretania Street. The
President’s house in Hawaii was in zip
code 96814 and the zip code for
Danbury, CT. is 06814. Since the '0'
and '9' on a typical typewriter are
immediately adjacent (remember, the
president's Social Security number was
issued in 1977, before the age of
computers), it would have been a
common error to accidently type a '0'
when the ZIP code really began with a
'9'. Another possibility is that
President Obama, a left-handed 15 year
old boy at the time, may have written
his own ZIP code in a
less-than-fully-legible manner, making
the '9' look somewhat like an '0'.