Some Japanese researchers have studied the relationship between selective mutism and school refusal.
Most of them have argued that selectively mute children don't generally refuse to attend school(for example, Sogame, 1973; Araki, 1979; Kawai, 1994).
But recent studies are lacking. School refusal today is different than the 70's and 80's (Kawai's study is based on studies in the 60's-80's).
Browsing the web, I found many stories of Japanese children with selective mutism who refuse to attend school.
I expect control studies. To carry out a control study, researchers need to gather children into two groups. One is composed of children with selective mutism. The other is control group that doesn't include selectively mute children. Then examine how many children refuse to attend school in both groups. Then compare both of them to examine whether significant difference exists or not.
In Europe and the U.S., control studies on selective mutism have been carried out. But in Japan, that have not.
[Related link]
Selective mutism and school refusal (The selective mutism journal/Japanese)
http://smjournal.com/ar071201.html
Index of SM in Japan