1) If you don't  have an employment contract, you are an employee at will, and could be fired for essentially any reason not specifically prohibited by law, such as illegal discrimination (e.g. against an employee due to his/her race, religion, age over 40, sex, or disability). There is no prohibition against asking for this form, so your employer should be able to terminate you  if you won't comply.2) If your made claims about your military service or separation therefrom which turn out to not be true--and which would certainly provide a good reason for the employer to ask about this form--then not only could you be fired, but you could be fired "for cause" (fraud or dishonesty) and denied unemployment compensation.The fact that you have been hired already has no legal effect.