said 1 year, 5 months ago:
this would not only apply to twitter but just about every social media platform.
if its personal threat, you still need to treat it as if it were a business threat (assuming you run your own business) as people digging around could stumble upon it, and your retaliation so it would have to be above board.
having said that, if the comments are truly threatening you could either delete / block them or speak to your lawyer. i would never recommend deleting a business related comment (even if its critical) but 100% personal ones, sure, seeking advice would also help i imagine.