Not necessarily.  You would have to check each states filing requirements - i.e. each state will have a set amount or set of scenarios where you have to file a return.  If you earned a small amount of income in a few different states, it will probably be true that you don't need to file and you can just forgo the small refund.  But, there could be exceptions.  For example, Pennsylvania requires all residents and non-residents who earned more than $33 in taxable income to file a return, even if no tax is due.