Many political theorists, philosophers, and International Relations scholars argue that states are ‘corporate moral agents’, which can be held responsible in many of the same ways as individual moral agents. States can have debts, contractual obligations, reparative obligations, and duties. Should states also be subject to criminal responsibility and punishment? Thus far, the debate about state crime has focused on two general problems with corporate crime: whether corporate entities can have intentions (or mens rea); and whether it is possible to punish them. In this paper, I identify two problems with extending corporate criminal responsibility to the state. First, since there is no ‘international corporate law’ that regulates the internal structures of states, many states fail to meet the conditions for corporate agency (and hence for criminal responsibility). Second, since the most serious international crimes are not subject to a statute of limitations, the argument for state crime paves the way for forms of ‘historical punishment’ that few of its proponents would accept. Finally, I argue that it is unnecessary to hold states criminally responsible, and that state responsibility ought to be understood as reparative rather than punitive.