The cooperative board of the San Remo on Central Park West has refused to let the rock singer Madonna buy a $1.2 million apartment.

The 26-year-old singer was advised by the San Remo Tenants Corporation Wednesday that she could not buy the three-bedroom apartment in the co-op between 74th and 75th Streets.

The co-op board did not give any reason for the rejection. The current issues of Penthouse and Playboy have nude photos of the singer.

''Maybe it's because of the fact that she's such a celebrity at this point,'' said Arlyne Rothberg, who is selling the apartment.