While I haven't heard anything about the DoJ related to the self-driving feature, how they might be involved is pretty obvious:

The DoJ prosecutes federal crimes, including, reportedly, a recent criminal referral from the SEC.

While the trigger for that was Musk's tweets, federal criminal investigations aren't narrowly restricted to the conduct which triggered them; Tesla has made representations, regarding the self-driving feature to investors as well as consumers; to the extent those representations did not fully accurately represent Tesla’s knowledge, and materially impacts Telsa’s expected costs and outlook, that's a potentially criminal securities fraud.