Oh my friend, yes you do. Even if it is a simple list of who gets called first.
And why? Because anything that enters social media streams about your company, true or not, can be discussed with a potential for escalation. And if there is a real crisis you need to be prepared to speak with the media.
A few things to consider: Who is the point person that delivers the message? Who is in the key team should a crisis arise? How and when do you reach out to your key stakeholders to keep them updated on the situation?
Get your crisis plan ready before you ever need one.