I am a 32 year old Assistant Professor. I met a girl at a conference. I liked her, but I realized she is a graduate student at the same university where I am faculty member. She is from the same school, but from a different department. Is it ethical for me to date her?
I hope it's ethical! (My husband was a graduate student at the university I'm a professor at, in a different department in the same school, when we started dating.)
The core ethical issue in faculty/student relationships is the power dynamic: it creates an ethical problem if you have power over her career, either in a way that could favor her (leading to concerns about favoritism) or disfavor her (leading to concerns about coercion).
In separate departments, that's not likely to be an issue: most assistant professors at most universities don't have power over graduate students in other departments. There are still situations where issues could arise - say, if you ended up on the panel choosing which grad student from the school would win a prize, and she were a candidate; or if you were asked to be the outside member of her thesis committee (at a school which picks outside members to be professors from other departments).
So, unless your school has a specific policy on the subject, it's probably ethical, as long as you make sure to avoid being in a position that creates a specific conflict.
You should check your school's HR handbook or department policy. Many institutions have specific rules. If you don't violate their rules, and the relationship is mutually agreeable, best of luck to you both.
I just ran across a publication from a very respected professor, at a very respected institution, who collaborates with his wife, also a professor at the same institution, and a co-author on the paper. His bio indicates he met his wife while on a fellowship.
I generally agree with other posters that separate departments should be distant enough--except that you met at an academic conference, which suggests your areas of study overlap in some way. How big was the conference, and has she already proposed a dissertation that does not overlap with your expertise? Further, depending on HOW you met (e.g., session vs. conference social), it might be murky whether her interest/expectations are about professional networking or a romantic relationship (or, problematically, both at once).
I am a fan of Stanford's recent policy on this. They created an infographic, available here: https://harass.stanford.edu/be-informed/guidelines-consensual-relationships. Basically, NEVER date undergrads, and teachers shouldn't date any student "when a teacher has had -or might be expected ever to have-academic responsibility over the other party." ("Student" here includes grad student, postdoc, and clinical residents/fellows.)
With what you know now, how much does your field fall within all the possible things she might think of studying? (Grad school is broad, after all...) If you study social psychology and she studies sociology of groups, say, you might have too much overlap to ethically date: she might have to curtail her academic interests to avoid taking your classes. (That said, it would be problematic on the other hand if you two developed an academic relationship with an unrevealed desire for a romantic relationship still lurking.)
Also consider what would happen if you dated but broke up acrimoniously. You would have to recuse yourself from judging things she was part of, but what would happen if her advisor recommended she take a class in your field of expertise?
Obviously, as others have said, it would be unethical to violate the expectations set up in your school's policies (unless the policies themselves were unethical, such as Bob Jones University's old ban on interracial dating). But presuming the relationship was OK by your school's policy and your fields of research are separate enough that you are not going to infringe, you might be OK.
You would have to think about how to ask her out directly, once, making it clear that you have no power over her and there would be no repercussions or hard feelings or pursuit if she said no. Or, better yet, hope that she asks you out! (Perhaps see social advice and workplace advice on the delicate question of HOW to / not to ask if you decide to.)
This actually breaks into two questions:
Is it Ethical? and Is it Okay?
The first is answered most easily by "Check with HR". I have been to universities where the answer has been "Absolutely not under no circumstances", and some where the answer has been "As long as you're not in a supervisory position".
Now onto "Is it ethical?"
In my mind, the biggest issue here is the potential power imbalance between the faculty member and the student, and the ability of the faculty member to influence her career and degree progress positively or negatively.
That comes up most directly in the same department or in a direct supervisory role, but it could also crop up if you're in the same school. For example, if there are school-wide awards, fellowships, etc. where you're potentially in the position to be judging her. Or if you're in a school where committees are often hybrids from several departments, etc. - which might be a thing if you met at the same conference, depending on how big and broad that conference is (for example, the American Public Health Association's annual conference is a massive, broad thing, while on the other hand a specialist conference might end in going 'Technically we're in different departments, but we both work on X', wherein there's a bit of a problem).
At the very least, it needs to be documented that it exists, and there should be a formal plan for how this isn't going to impact her progress. There also needs to be an acknowledgement in both your minds that this is a dynamic question - as your career and hers progress, it may be important to revisit the question and make sure no conflicts exist, and evaluate opportunities that come up in light of your relationship.