If the campus police is a real police department, it will go through the usual police and criminal justice system. In such a case, whether the campus police or the city / county police has primary jurisdiction depends on where the incident occurred. If the campus safety department is not a real police department, someone who wants to report an incident to the police needs to contact the city / county police.
A university administrative process would involve reporting to a different entity, with a different process separate from the criminal justice system.
A third avenue is a civil lawsuit.
These are not mutually exclusive. Standards of proof and potential penalties for the accused differ. (So can the competence of any investigation by any third party.)