As officials at Columbia University pitch tents and plan speeches for the school’s annual commencement ceremony, they are also facing questions about whether one famous student will bring her mattress to the event.

Emma Sulkowicz, a senior at the Ivy League school, says she was raped by a fellow classmate in her dorm, but that the classmate was cleared of the crime in a flawed university disciplinary proceeding. She has vowed to carry her mattress as part of a school-sanctioned art project called “Mattress Performance (Carry...