From 2005, Peter Sandman, a Risk Communication Specialist (a job title I've never heard of), says that actual panic is rare:
But official "panic panic" is common. That is, officials often imagine that the public is panicking or about to panic. And in order to allay panic, officials sometimes do exactly the wrong thing from a crisis communication perspective: They withhold information, they over-reassure, they express contempt for public fears, etc.
(hat tip: Robin Hanson)