Okay, here's what the National Center for Transgender Equality (
http://transequality.org/Issues/federal_documents.html) has to say about changing your gender on Social Security (which, btw, is a national entity, so its policies are the same no matter what state you're in):
Gender ChangeTo change your name in the Social Security Administration (SSA) records, provide the following at your local SSA office. All documents need to be originals or certified copies by the issuing agency. You can find the nearest SSA office at the Social Security website.
1. A completed Form SS-5 "Application For A Social Security Card." (
http://www.ssa.gov/online/ss-5.pdf)
2. Proof of identity. One or more identity documents in your new legal name, such as, a driver license, passport, state-issued ID, etc. These documents must show your current legal name.
3. A letter from the surgeon or attending physician verifying sex change surgery has been completed. This letter must clearly identify you as the person changing their gender marker.
4. If you are a U.S. citizen and have not previously established citizenship with SSA, you will need to present a birth certificate, U.S. passport, or other proof of citizenship. Note: your birth certificate or other document establishing citizenship does not need to show your current name or gender. However, you will need to show proof that you are the same person, such as with a court order for legal name change.
5. If you are a non-citizen, you will need to show documentsproving your immigration status and work eligibility, such as, Form I-551, I-94 with unexpired foreign passport, and/or work permit card (I-766 or I-688B). Because there are many types and combinations of qualifying documents for non-citizens, you should call SSA to confirm that your documents qualify.
But yeah, some of it may come down to the individual Social Security employee you're working with. I haven't had surgery, so I haven't tried to change my gender in their system, but when I went to show them proof of my name change, the guy I talked to needed some convincing that it was okay for me to change my name from a traditionally female name to a traditionally male name, even though I had a court-ordered name change with me. It might be a good idea to go into the Social Security office with a copy of the official policies on hand with you, just in case you need to back yourself up. The Social Security webpage with its official policies on this topic is here:
http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/1667/~/correct-or-change-gender-on-your-social-security-record