I'm not a cop, but I have done a polygraph for work. It can definitely be uncomfortable because you have to control your body in a very specific way, but just do your best to comply with what they ask of you. Worst case if you "fail" is that they'll most likely just re-schedule you, pushing your timeline a bit to the right. Let them know you have a stutter & be up front about whatever weird personal quirks that come along with it. They're professionals & should understand. You'll be alright.