Police say a Carnegie Mellon alumnus fatally shot his graduate student girlfriend before committing suicide inside their off-campus apartment.

Pittsburgh police found their bodies at about 1:45 p.m. Thursday after a friend asked authorities to check on the woman's welfare.

The woman was identified as 26-year-old doctoral student Chalalai Chaihirunkarn (sha-lah-LAY' SHY'-run-karn). She studied computer science. Police say she was shot several times in the head and chest.

The man was identified as 29-year-old Bryan Springer. He graduated in 2007 and worked at CMU's Software Engineering Institute.

Police Cmdr. RaShall Brackney says friends told police the couple's relationship was troubled, but there were no signs of a struggle.

Police and the medical examiner are trying to determine when the shooting occurred. Friends said they hadn't seen the woman for days.