How to respond when insulted by a grad student in a different department? I'm a lecturer at a small university. In a class I taught last year, one grad student disagreed with his grade and complained as high up in the university as possible. The result was the grade stayed the same. 

I see this student on campus from time to time, and he usually ignores me, which is totally fine. However, this week I saw him on campus and as he walked by he said something insulting. Nothing awful but certainly disrespectful (along the lines of "you suck"). The student was also disrespectful during class. I'm thinking about discussing this with the chair of his department. Is this an over reaction? What would an appropriate response be (if any)?
I'd probably document it (make a dated note to yourself someplace noting what occurred and exactly what was said, while you still remember it) and then ignore it, unless it becomes a pattern. The purpose of documentation is to start a record in case the behavior turns into something more regular.

The exception I would make is if you have any reason to believe this student is abusive/insulting to anyone vulnerable or deserving more protection. For example, if the commentary is racist, sexist, homophobic, etc. If it's more of a "(expletive) you" I'd let it go.