A frantic New York University (search) student yesterday ran from her family's Greenwich Village apartment saying, "Don't tell my father" — before racing to the roof of her graduate-school building and jumping naked 12 stories to her death.

Joann Leavy, 23, is the sixth student at NYU to take a fatal leap in the past year.

Leavy, a second-year film student, ran out barefooted, then peeled off her clothes while racing up to the roof of the Tisch School of the Arts (search) roof, law-enforcement sources said. Once there, she stripped off her panties and leaped, landing on Mercer Street just a half-block from her family's apartment on Waverly Place, sources said.

The middle child of three, Leavy had a history of mental problems, the sources said. But it is unknown what prompted her to take her life on a sunny morning just a day before NYU was set to start its fall term.

Just before 10:30 a.m., as students enjoyed the street scene near Washington Square Park (search), Leavy, wearing a skirt and top but no shoes, ran past superintendent John Lemieszewski and doorman Eddie Dihanpat and out the front door.

"She ran out . . . kind of in a frantic way," Lemieszewski said. "We found it odd that she just blurted out, 'Don't tell my father, don't tell my father,' because she never said anything to us before."

Cops said Leavy then dashed around the block and into the front door of the Tisch School at 721 Broadway, where she climbed the stairs and jumped minutes later.

"I heard the [noise], and I went outside," said a manager at Caffe Pane e Cioccolato on Waverly Place. "It was terrible, and I was distraught. I wish I hadn't seen it."

Lemieszewski said he learned Leavy had jumped after police arrived at his building to get the woman's father from his apartment and take him to the scene.

"He was like all sobbing and couldn't believe what happened," Lemieszewski said.

Leavy lived at the building with her parents, brother and older sister, workers said.

The super said she and her father "on certain occasions don't get along" and that in the past, she'd left the building in a huff after confrontations with him.

After Leavy's broken body was taken away in an ambulance, someone left a bouquet of flowers where she had fallen.

NYU spokesman John Beckman said, "Her death is a matter of great grief for the NYU community and our sympathies are with her loved ones."

He said the university planned to offer counseling at two of its residence halls last night and also would tell Leavy's classmates about her death.

NYU this year began offering a 24-hour counseling hot line and mandated a mental-health services orientation for freshmen because of the rash of death leaps by university students, which began last September.