It does in a way but it definitely isn't purely genetic. I'm one of an identical pair of twins, but my twin brother does not stutter the way I do - he claims to have overcome it but I cannot remember a time when he used to stutter. My younger brother does stutter but no one else does in my extended family except a first cousin through my father's side and a second cousin through my mother's side. Interestingly all the stutterers I know (including two from school and one elsewhere) are male??