Can you declare bankruptcy for overpayment for unemployment?

You probably won't get any protection/relief for that. First, overpayments and amounts due to most governmental agencies are given a very high priority. Second, and more importantly, is that under almost any instance of you receiving unemployment that you weren't supposed to, it is because of your filing a claim that you weren't alllowed to, or hiding your current employment of such, all of which to collect you swore something different, and is actually able to be pursued as a fraud and crime. The agency is giving you a break allowing you to make it good. Illegal acts, like fraudulently getting UI, are not going to get any protection by the BK court.