In most cases, campus safety would contact the local PD department, if it appears a crime has occurred that would lead to possible prosecution, such as sexual assault.
Even colleges that have their own PD departments, don’t have investigators, forensic specialist (CSI for the Win!) or prosecutors. They may deal with rowdy students, stolen items, etc., but anything that may lead to a criminal case, would involved the local police department.
Of course, sometimes they don’t involve the local PD, when they should, which usually leads to the scandals we read about in the news. However, it’s not the policy to “cover-up” crimes.