The Supreme Court has been asked to decide whether Virginia denies equal protection of the laws by exempting from it obscenity statutes publicly financed institutions, including universities, museums, libraries and theaters.

The case originated last year in Richmond, where Broadway Books Inc. went into Circuit Court to seek a judgment whether commercial showings of the X-rated film "Deep Throat" would violate the statutes.

Judge James E. Sheffield upheld the exemption and, in turn, was upheld by the Virginia Supreme Court. Now Broadway has asked the U.S. Supreme Court to review the ruling.

In the brief for Broadway, Burton W. Sandler of Baltimore found "the epitome of capriciousness" in showings of "Deep Throat" by university of Virginia students who charged admission. Thus the state "allows one party to commit an offense with impunity while treating the same act by another as criminal," Sandler wrote.

In the state's brief opposing review, Attorney General J. Marshall Coleman said Broadway presented no evidence from which Sheffield could have concluded "that the motion picture shown in Charlottesville was in fact the same as the one shown in Richmond."

Moreover, Coleman wrote, students - not the university - had shown the film, whatever it was, and "were subject to the same provisions" of the statutes as Broadway.

In his opinion, the judge cited numerous decisions of the State Supreme Court holding that classifications created by the legislature are presumed to be constitutional so long as they are "rational" and promote "a legitimate state interest." Here, he said, these amount to Virginia's "right to protect society's interest in order and morality."