What constitutes workplace slander? How?

I am a female employee of a local government agency. Recently I was appointed as interim supervisor during a transition period. Office gossip began that I slept with the director to get the appointment. I took it as nothing but office gossip until at a team meeting a female member of our governing body repeated it in front of the entire team. To have office gossip repeated by our agency overseer in a public forum was at the least unprofessional and some were so infuriated they suggested it might be slander or defamation of character. I would just like to be armed with the legalities before I ask for an apology.