The student was sitting on a bench on campus near South Seventh and East San Fernando streets sometime between 9:30 a.m. and 10 a.m. when the suspect offered her the cigarette, university police Sgt. Robert Noriega said.
He then lured her into the alcove of a nearby building, where he groped her and tried to keep her from leaving, Noriega said.
She was able to break free and caught a bus nearby, but the suspect followed her onto the bus, Noriega said.
The suspect eventually got off the bus, and the victim rode the bus to the end of the line at Capitol Expressway, then reported the incident to police at about 11 a.m.
Police are now looking for the suspect, who is described as a black man in his 30s, about 5 feet 8 inches tall, with buck teeth and crooked lower front teeth. He was wearing a blue shirt and black pants.
An alert was sent out to students Monday afternoon notifying them of the incident, Noriega said.
Anyone with information on the case is asked to call SJSU police at (408) 924-2222. Those wishing to remain anonymous can call (408) 337-2919 or email firstname.lastname@example.org.