Are employers required to conduct a sexual harrassment investigation prior to terminating an employee?

I have been wrongfully accused of sexually harrassing a fellow co-worker. The accusation is 100% baseless and completely false. Needless to say she, and yes I'm a guy, brought it to the employer's attention accusing me of saying something inappropriate and now I have been arbitrarily terminated without any sort of review or even asking me if I even said anything to her. It's just like bam, she says you said something to her so you're fired. I've looked in many places and some say that companies are required to investigate sexual harassment accusations, but all of those sources of information are referring to the victims rights. What about the rights of someone that is wrongfully accused and then subsequently terminated without the benefit of even addressing the accusation? So that would be my first question and the second is are employers required to conduct an investigation or at the very least offer some sort of rebuttal opportunity to the accused?