Depends on what you mean in terms of "nasty". Nasty as in .. A). chewing someone out for no real reason ... or Nasty as in B). hitting/attempting to hit/personal property damage, ect?
In the case of A). most people that are depressed, that I've seen .. myself included, will often lash out more easily than a person who isn't depressed. Depressed people have a lot on their plate, and sadness will easily turn to anger under the right circumstances. Anger just seems like a lot easier emotion to "control" than sadness is. It also lets you feel something besides the sadness, since happiness ins't really an option, per say.
In the case of B). I would say not, exactly. It's more than likely more of a trigger based off of the depression .. those type behaivor issues are likely something that was already there (temper issues) before the depression set in, and the anger release triggered by the depression outbreak is just fanning the already lit fire within.