JUST want your SSN?? This is truly very dangerous. There's a similar phone scam where the caller says that they're from the local board of jurors and you're being arrested for not showing up for jury duty. When you protest that you never received a notice, they ask for your SSN so that they can clear up the mess. BINGO! Now they've got you.

You should save that email, print it out, and bring it to your local branch next time you go to the bank. Even if you verify its authenticity, it's still a horrible policy for banks to be sending out messages asking for SSNs.