Well I know now for a fact that they do check your criminal history because I have had people tell me first hand that some have been turned away at the border with dui's that didnt know about the laws before they drove all the way up there. The only way they were let through was by filling out a set of $200 temporary citizenship forms, which is basically just a bribe. And Ive heard that even with those forms, you are still under the discretion of the border officer whether you get in or not.