It depends completely on what you're calling a misdemeanour, and how long ago it was, and how you're going to be able to explain it when you're asked about it should you reach any kind of interview stage. If you have been in trouble for taking drugs but can convince them that it was when you were a teenager and pressured into it, and that you haven't done it since, then there is a chance that they would overlook it. If, however, it was to do with you attacking somebody for no reason and you were charged for it then this is different and altogether more serious, and certainly not something that it would be likely for them to overlook in order to allow you to become a police officer.