Guess what? They do. From ABC News, regarding the VA Tech shooter:

Some news accounts have suggested that Cho had a history of antidepressant use, but senior federal officials tell ABC News that they can find no record of such medication in the government's files . This does not completely rule out prescription drug use, including samples from a physician, drugs obtained through illegal Internet sources, or a gap in the federal database , but the sources say theirs is a reasonably complete search.

And in fact, the article suggests that this isn't just a database of patients who use anti-depressants, it's a federal database of every prescription drug you've ever bought.

We don't even have a list of gun owners, and we have a list of everyone who has been prescribed anti-depressants?What exactly do the Bushies do with that list? And what other lists do they have of which medications you've ever taken?