Teacher falsely accused of sexual assault of a child. Teacher was reassigned to original position.
Constitutional Law Attorney
If a person has the funds to afford an attorney, or the will to take the task on without an attorney, YES, a teacher can sue a parent for defamation.
In fact, just about anyone can sue just about anyone. As a consequence the victimized defendant of potentially fraudulent and possibly misguided litigation may incur the costs of defending themselves against such suits.
I think the better question is either WILL a teacher sue, or SHOULD a teacher sue.
More details might help to provide more of a discussion. For example, under what circumstances was the accusation made? It's one thing to publish such accusations in a newspaper; it's another thing entirely to repeat the allegations on the witness stand.
If you are the teacher, contact an attorney to evaluate your potential case; if you are a parent, contact an attorney to assess the defensibility of your actions.
This answer is not a substitute for consulting with and retaining the services of an attorney for your legal needs. By providing this answer, I am not entering into an attorney client relationship with you.