Officers responding to a report of shots fired found Carson's body early Wednesday in a quiet residential area in Chapel Hill, The Raleigh News & Observer reported. Police Lt. Kevin Gunter said Carson had been shot several times in the head.
There were no keys or other identification on the body. Carson was last seen alive at about 1:30 a.m., several hours before her body was discovered. Her roommates said she often went to the student government office to work in the middle of the night.
"At this point what I'm thinking, what it feels like, is a fairly random crime," said Police Chief Brian Curran.
Carson's car was found Thursday afternoon. Police told NC Wanted that the Toyota Highlander was parked in a residential neighborhood within a mile of Carson's home and not far from where her body was discovered.
Carson, from Athens, Ga., was a senior. She was a member of Phi Beta Kappa and planned to go to medical school. As student body president, she sat on the university board of trustees.
Chancellor James Moeser, who led students in a brief memorial Thursday afternoon, called her "a wonderful person and a great friend."