A staff member was rude to me in an email and made me look bad in front of other members of the staff. How should I handle this? Due to some unfortunate miscommunication, one of the staff members at a university felt like I did not meet one of my obligations.

The staff member sent me an extremely rude email that happened to include other members of the department who I happen to know personally. The fact that the email was extremely condescending makes it seem like the staff member was trying to make me look bad.

Several months ago I received an email outlining some obligations. About a week ago I received another email explaining that I did not have to do one of those obligations. (Fortunately, it turned out to be something that was relatively simple and could be done at any time.)

Because I did not think I had to do the obligation, I did not do it. If the staff member would have clarified what they said, I would have been more than happy to do it. It also turned out to be something extremely simple.

Instead of clarifying, they sent an email that said "I did your work for you" and "here is what I said several months ago to prove that you knew you had to do this" but did not mention where they said "you do not have to do this".

The email was extremely rude and condescending. I would have been able to let it go if they did not include the other members of the department in the email. Now I am not sure how to respond. My thought is that they just forgot that they said I did not have to do the obligation.

I am not sure how to handle this. I have ideas along the lines of asking for an apology, clarifying the situation and explaining that I felt they were extremely rude, or forwarding the entire email chain to higher members of the department.

If I do decide to ask for an apology or clarify the situation, I can't decide whether or not I should include higher members of the department or who in the department I should include.
It sounds as if your co-worker was extremely rude, and owes you an apology, but pointing those things out in so many words is rarely productive. Instead, I would use something like the following template with a reply-all:


  Hi John, there seems to have been some misunderstanding. From your
  email of January 28th (copy attached below), I understood that I was
  no longer required to feed the departmental axolotls - if I misunderstood this, could you please clarify what was intended? 
  Anyway, thanks for fielding it on this occasion. 


At that point, if your co-worker is a sensible person who was just having an off day, they will offer an apology without further prompting. If not, well, your other colleagues can form their own judgement based on the relevant facts.

edit: 

re. whether it's better to respond to the CC list, or just in private: you certainly have a right of reply in the same venue, but whether it's advisable to exercise that right depends very much on circumstances. 

If the alleged omission is sufficiently trivial ("you didn't wash up the teapot yesterday!") then "John" has already made themself look silly just by making a big deal about it, and it's not likely to harm your reputation, so I'd just let it go. The annoyance value to others from prolonging the thread outweighs any need for reputation control; cf. the old adage about wrestling with a pig.

At the other end of things, if leaving the allegation unanswered could harm your professional reputation ("you didn't label the poisons cabinet/feed the research animals/complete the grants proposal due next week"), and if "John"'s allegation might seem plausible to the recipients, then it becomes important to rebut it in the forum where it was made. You don't want a dozen co-workers believing that you're a menace to their health or their work.

Leaving aside your own reputation, it might be important to reply for other people's sake. People take their cues on acceptable behaviour from those around them, and bullies often bully more than one person; for either of those reasons, it can be beneficial to see bullying behaviour promptly challenged. 

Because workplace culture varies so much, it might be wise to seek input from colleagues at your institution - they can probably tell you better than us whether people take your co-worker seriously.