My advice is document the incident including the day, date , time and students name and report it to your department head and say nothing to the student. And if it continues follow the same procedure in case you are getting set up for sexual harassment.
Without a doubt, this is the proper procedure. No matter what happens next you are covered. I have good reason to believe nudeyorker knows what he is talking about.
I know as a teacher this is what we were told to do in public schools. I wouldn't think it would be any different in college.
Yes, the girl is over 18. She could claim you raped her and you could still go to jail. Her being 18 doesn't protect you from the teacher/student relationship etiquette that is expected of the professors.
You need to be able to pass a lie detector test that indeed you never spoke to the girl about this, nor wrote her anything about it.
If she makes suggestive gestures in class or anywhere else, I would walk away immediately making no eye contact nor any vocal response and IMMEDIATELY report that you your the proper officials at school.
If she weren't in your class, the rules would be totally different. College professors are often hired for the knowledge of the subject material and those professors have had absolutely NO "staff development" classes in professor/student relationships. What is proper. What is not.
Perhaps you need to ask for such a course or at least a manual to read about the subject, student and teacher relationships outside the classroom.
To some who who may not know, it is improper for a student to date the teacher during the time the student is taking the class. If the student and teacher are already dating, this must be pointed out to the appropriate dean and a decision made to whether this can be allowed. Even a married student would have to get special permission to take a class taught by their spouse. The reasons are obvious. We have already heard a lot about the grade issue. The other is the issue of a teacher taking advantage of the teacher as in "if you want to pass this class, you have to put out for me. But you have to pretend we are really dating."
In a situation where the teacher is the spouse, often the spouse's partner takes a test made out and graded by another faculty member or at least the paper itself is graded by another faculty member.
No the above will not fix the problem entirely. However, the more steps we take to guard against abuses, the better our likelihood of preventing abuse of some kind regardless of the type, sexual, fake grade, etc.
Concerning the problem of the girl being reported when she is innocent. Yes, that can be a problem if this isn't handled properly. What is SUPPOSE to happen is nothing except this is in this teacher's file, not in a file for the world to read and unless something else comes up about it, it is suppose to be strictly confidential. If there is a leak about it from the college officials office, then the school is ripe for a big law suit from both the professor and the student.
The laws on confidentiality concerning issues like this for school officials are very clear and firm: Don't repeat information about students and teachers that is suppose to be confidential. You could among other things lose you job.