As someone in a clinical psychology graduate program, I doubt there's a connection. Both conditions are diagnoses in the DSM but one is an anxiety disorder (OCD) and stuttering is not, although stuttering can cause anxiety and anxiety can cause a stutterers severity to increase. Stuttering is not a emotional disturbance phenomenon, nor is it any kind of indicator of psychological vulnerability or weakness. However it is a risk factor for psychological disorders, particularly anxiety disorders and mood disorders, e.g. social anxiety disorder, panic disorder, major depression. A stutterer is not obsessed with fluent speech (or anything) in the way a person with OCD would be, nor is stuttering the result of a compulsion to reduce dysfluency. I wrote my Master's thesis on the topic of stuttering and found no research that even mentions a correlation between OCD and stuttering as a possibility or a potential phenomena. They are fundamentally different things. One last thing tho, I could see someone who stutters having a higher likelihood of developing OCD due to the trauma of stuttering in our culture and perhaps some way to cope with the trauma may manifest itself as OCD - however this is my personal conjecture, as I said before the research I found never mentioned a OCD diagnosis being any more prevalent for people who stutter then the general population.