I am a graduate student with an assistantship. I met an undergraduate and we hit it off (talking about sex, but not sex with each other). But now I assist a class with her (and I'm not good at hiding my feelings) and she is very flirty. She also put her hand on my arm outside of class (which was welcome). I am performing my job, but I am worried that if things go bad with us she'll claim sexual harrassment. What should I do?
I am performing my job, but I am worried that if things go bad with us she'll claim sexual harassment. What should I do?
Don't let things go bad. I.e., stop talking about sex, try to hide your feelings, don't flirt, etc. As long as she is in your class, you have a professional obligation to treat her the same as your other students, regardless of whether she welcomes your interest. Doing anything else is dangerous. (Even if she makes no complaint, other students may raise the issue with the administration, if they are upset by it or suspect favoritism.)
In principle, you could try to change your teaching assignment to another class. However, I'd strongly recommend against asking for this. It might not be possible (maybe there's nobody available to switch with you), in which case you'll be in a real mess if you have implicitly announced that your current assignment is untenable. Any changes will be disruptive, which will annoy the professor teaching the class as well as whoever handles the teaching assignments or has to switch with you. Plus the teaching change will be public enough that it will probably create rumors of impropriety.
As a female student who is currently VERY interested in one of her TAs, I have to agree with what everyone is saying: DO. NOT. ENGAGE...
Wait until you are no longer teaching her (and there is no chance that you will ever again teach her), then feel free to accept any invitation to coffee. Asking her to coffee yourself could be risky, if it turns out that she is not as interested as you think. If she likes you as much as I like my TA (who has unconsciously also displayed interest in me, but has been very careful to not show said interest... I have no way of knowing if he is actually interested until after the term is over, when I plan on asking him out), then she will ask you out after the term is over. If she does so beforehand, politely explain to her that it would be highly inappropriate.
At this point, it's not even smart to tell her to wait until the end of the term, because you would still be implying that you like her. You have to act uninterested until the term is over. Period. She will get it. And she will wait. Be patient, and don't obsess or it will show.
Under the assumption that you're in the US, it may be the case that you've already violated your school's policy on sexual harassment. It's important to recognize that quid pro quo harassment does also constitute sexual harassment under most (if not all) school harassment policies. Simply put, quid pro quo harassment occurs when a person incentivizes engaging in sexual or romantic activities with him or herself in the workplace. Again assuming that you're in the US, quid pro quo harassment is most likely prohibited by your college's sexual harassment policy. Title IX generally requires college's to have such policies.
As someone who is in a relative position of power over this student, any attempt to initiate or maintain a relationship with her is almost certain to be a violation of your school's policy, and could end up having quite serious implications for you, regardless of how your hypothetical relationship plays out. While you may view this student as being the initiating party, as the person in the relative position of power, it's your responsibility to set boundaries.
From your question, it's not clear to me exactly where you are getting the idea that this person is interested in initiating a relationship with you, so I would avoid broaching the subject directly, however you need to stop any further discussions of the sort you mention as soon as they come up by saying "I'm sorry, but that's not an appropriate topic for us to talk about". It isn't exactly what you're asking, but I can't help but notice that I don't see any evidence from your question that she's actually interested in having a relationship with you anyway. You say that you had a conversation where sex was mentioned, and that she touched your arm once. Neither of those things to me necessarily imply "interested in starting a relationship", though of course there may be other reasons that aren't in your question.
Other commenters here have suggested trying to switch teaching assignments, however I would suggest that that will not entirely mitigate the power differential necessary for quid pro quo harassment to occur. The best way to prevent her from claiming sexual harassment, is to not commit sexual harassment. It's not the answer that I think you want to hear, however it is the answer that you're likely to get from your school's HR/Title IX department.
Talk with your Professor about this. Depending on the course, the Professor may have some leeway in having another TA take over the grading of her materials and interactions with her, etc.
And if not, it would be good to have your concerns "on the record."
You are very right to be concerned, but you don't have to make decisions (on how to handle the concern) all on your own.
In addition to Anonymous Mathematician's fine answer, I'd also recommend that you also take steps to make sure that all of your future interactions with students are in public places where witnesses will be present. For instance, hold office hours in a library or café instead of in a private office. Note that this would be a general policy for all of your students, not just your interactions with the student in question.