I left the military in 2000 and now I received a letter, asking me to repay over $600, that I allegedly owe due to an "erroneous final payment dated June 2001 on an overpayment of the May 2001 mid-month".
I should not have received any money then and I'm pretty sure I never got that payment at all, but it was over 5 years ago and I have no records left...
Is there a statute of limitation on an overpayment of salary? Even though it is the government?

I understand that this is a frustrating situation for you. As you are aware, the government probably does have records of this so you may want to speak with an attorney to discuss your legal options. You can locate one through the attorney locator on Lawinfo's home page at http://www.lawinfo.com/. Some do offer free consultations.