Officers first received received reports of a shooting at 12:53 p.m.
When the arrived at Building N of the complex, they found Tyrone Xavier Hester, 25, lying in the grass behind the structure. He was pronounced dead at the scene.
Hester's daughter, Aaishia, was critically injured. The 22-month-old was taken to Duke University Hospital, where she was pronounced dead.
Investigators believe Hester shot his daughter once, then shot himself. They say Hester did not live at the apartment complex, but was there visiting relatives.