Detectives were closer Wednesday to learning why the suicidal ex-boyfriend of the daughter of a New York University faculty member killed the young woman and left her decomposing body in a campus apartment, police said.

The body of Boitumelo McCallum was found wrapped in a sheet in the locked bedroom of an NYU apartment Sunday after tenants noticed an odor.

Her former boyfriend, Michael Cordero, was being sought for questioning when he went to the roof of a housing project late Tuesday and slit his wrists, police said.

"I tried to kill myself because I killed my girlfriend," Cordero, 23, told workers at St. Luke's-Roosevelt Hospital Center, police spokesman Paul Browne said.

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He was in stable condition and was being interviewed by detectives at the hospital, authorities said.

Police said they believed Cordero was at a party at the apartment that began Wednesday night and continued into Thursday, the day McCallum likely died.

"She was his everything," Cordero's sister, Diana, said of her brother's relationship with McCallum.

McCallum's body, which had decomposed in the warm weather, had "some damage to the face — a possible fractured nose," police Commissioner Raymond Kelly said.

An autopsy was performed Monday, but the medical examiner said more testing was needed to determine the cause of death.

McCallum, 20, was described as a "bright and talented" student at Mills College in Oakland, Calif. She held a South African passport.

McCallum's mother, Teboho Moja, is a professor who has specialized in globalization and its effect on higher education. She also has served as a policy analyst for the South African government, according to an NYU Web site.

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