University officials on Monday identified the victim as varsity cheerleader Paige Raque.
Authorities said she fell 39 feet to the parking lot below at the Calder Commons building in downtown State College overnight Saturday.
State College police have said the fall appears to have been accidental but an investigation will continue.
Penn State's gymnastics coach Randy Jepson is acting as a spokeswoman for the young woman's family. He said Raque suffered a traumatic brain injury and her family is at her side.
Raque is a 2011 graduate of Christian Academy of Louisville in Kentucky. Her brother, Parker Raque, is a Penn State gymnastics team captain and student.