For cases that are adjudicated not under Title IX, colleges and universities are free to choose their policies as to how they believe appropriate to address and adjudicate sexual assault, sexual misconduct on campus. Different schools are going to have different policies. There may be variations on a theme in a sense of some schools will allow a hearing, some schools will not. Some schools will allow for any cross-examination. Some schools will allow in-person cross-examination. Some schools may not allow cross-examination at all.
Again, these are for cases that are pursued under the school's non-Title IX sexual misconduct policies. The school is free to choose its own policies, because of that some schools are going to be more, say, cognizant of an accused party's interests and rights, other schools are not, but either way it's very important to have an experienced attorney advisor help you navigate the process. They can best understand how to approach any policy at a given school and how to best defend a person's interest.