I believe that the roadster has an open differential, and that it has been documented here on TMC.
Of course, I don't know why, but with all the trials and tribulations Tesla has just to get a working transaxle, first with Xtrac, then Magna, before Borg Warner stepped in and saved their bacon, I doubt there was any time to consider enhancements like limited slip or computer controlled diff lock.
I would be careful about retrofitting a limited slip as well, due to the tendency to induce oversteer.
GSP