The Fairfax County Board of Supervisors, steaming over the county library board's decision to continue lending cassettes of R-rated movies to minors, yesterday asked the library board to start requiring borrowers to show identification proving they are at least 17 years old.

The board of supervisors, which has control of the library system's budget, harshly criticized the library board's recent refusal to comply with the supervisors' request to restrict access to cassettes of such films as "Body Heat" and "Halloween."

"I think they showed poor judgment in spending $62,000 of taxpayers dollars in purchasing R-rated cassettes, considering we're short of research material," said Democratic Supervisor Martha V. Pennino, who represents the Centreville District.

"Even the motion picture industry, which is extremely liberal, has seen fit to restrict" some movies, she said.

Library officials have said that the total value of the county's collection of 1,200 films is about $70,000. No figures were available on how many of those films are R-rated.

Pennino initially complained to the library board about lending the films to minors, but the board concluded in April that it was the responsibility of parents, not the library system, to monitor what youngsters view and read.

County Board Chairman John F. Herrity said he was "very concerned that the library board doesn't understand" the seriousness of the issue. "They're thumbing their nose at the Board of Supervisors and I resent it."

Herrity, a Republican, warned library officials not to "take this action lightly."

Fairfax Library Director Edwin S. Clay said the 11-member library board, which is scheduled to meet on June 15, "will certainly reconsider the policy as they requested." The county libraries lend the cassettes free, to library card holders, for one day and charge a $1 a day late fee until the tape is returned.

County officials say that the supervisors lack the legal authority to actually require the library board to impose the age restrictions.

The debate in Fairfax reflects similar controversies across the country. Some say that age restrictions amount to censorship. But advocates of age limits argue that films are far more graphic than books and thus more harmful to minors.

In Alexandria, library patrons of R-rated cassettes must produce driver's licenses proving they are at least 17. Borrowers in Arlington and Prince George's counties must be at least 18. Montgomery County has no restrictions. Video cassettes of documentaries and children's films are available at the Martin Luther King Library in the District but cannot be checked out.