Yes, the University does maintain rules about intimate relationships between professors and students (both undergraduate and graduate). The rules prohibit intimate relationships between professors and students wherein the professor "has direct evaluative or supervisory authority over" the student. The University prohibits these relationships because it can create a conflict of interest for the professor. Two different policies prohibit the practice: SUU Policy # 5.27 and SUU Policy # 6.28.
This policy would also apply to coaches and employment supervisors.
If you have concerns related to this policy, you can contact the Office of the Vice President for Student Services at 435-586-7710.