Hundreds of New York buildings, including Madison Square Garden, parts of the World Trade Center and Chase Manhattan Bank headquarters, and seven State University of New York campuses, contain possible dangerous levels of asbestos.

According to report done in 1971 by the Mt. Sinai School of Medicine made public Friday, an asbestos fire-proofing compound was sprayed in many of the large buildings constructed during the 1950s and 60s.

The binding material, which kept the asbestos from flaking off, has deteriorated and there is the danger that asbestos fibers are mixing with the air in the buildings' ventilation systems, according to Walter Hang of the New York Public Interest Research Group.

Secretary of Health, Education and Welfare Joseph A. Califano Jr. highlighted concerns about asbestos Aug. 18 when he wrote to the nation's governors urging them to look into possible problems in their states.

"The Public Health Service has advised me . . . that any exposure [to asbestos] probably carries some risk of disease," Califano wrote in alerting the governors that levels of asbestos far lower than that permitted by the Occupaional Safety and Health Administration are potential causes of cancer.

The Mt. Sinai School of Medicine, in reporting on asbestos problems, has said that there are no technological barriers to removing flaking asbestos or sealing it permanently in place.

In the early 1970s, the dangers of spraying on asbestos fireproofing compound became known and builders stopped using it.

The World Trade Center was partially completed when the dangers were learned, so asbestos was used only on the lower floors of the two towers.

According to figures gathered by William J. Nicholson and Arthur M. Rohl of Mt. Sinai, 1.3 million pounds of asbestos compound were used in eight office buildings. The compound is 30 percent asbestos, 60 percent other insulating materials and 10 percent binder.

The disclosure of possbile asbestos hazards in dozens of office buildings followed the forced colsing of two Harlem grade schools where asbestos was found flaking irom the ceiling.

Cancer caused by asbestos exposure usually takes 30 years or more to develop, so children are particularly likely to become victims of such exposure.