An open conflict has broken out between the Fairfax County school board and some members of the Board of Supervisors over who owns surplus school sites.

The school board says it owns the sites and wants the supervisors to pay fair-market value for five parcels soughts by the county park authority as recreational land. The parcels, located in heavily populated areas of the county and totaling 92 acres, are appraised at $1,749,660.

Three supervisors - chairman John F. Herrity (R), Joseph Alexander (D-Lee) and John P. Shacochis (R-Dranesville) - argued at this week's board meeting that all land acquired through the sale of general obligation bonds belongs to the county, not the school board.

The five surplus sites were all purchases with such bonds. They are Chesterbrook Woods Elementary in Dranesville, Collingwood Elementary in Mount Vernon, Idylwood Elementary in Providence and Pinecrest Intermediate and High in Mason.

In sharply worded debate, Shacochis said, "This land is owned by the county and title should be held by the Board of Supervisors, and we should make the transfers as we see ift."

County Executive Leonard Whorton, in his recommendation to the supervisors, avoided getting enmeshed in the controversy over who owns the land by proposing that the school board simply transfer title for the sites, free of charge, to the county.

But that is unacceptable to the school board, chairman Rodney Page told the supervisors at their meeting. Page said that if public agencies, such as the park authority, don't want to buy the surplus sites at current market value, then the school board would sell them to private buyers.

In a memo to Whorton earlier this month, Superintendent of Schools S. John Davis, said, "The sites . . . are in fact school assets which in good conscience should be converted only to other school capital improvements . . . The diversion of school capital assets to other purposes, such as permanent parks, simply means that we must return to the voters and ask them for additional school improvement funds . . .

For both the school system and the county government, the issue is not only one of principle but of money. Both are feeling the crunch from last year's "no-growth" county budget.

In an attempt to break the impasse, Supervisor Alan H. Magazine (D-Mason) offered a motion under which the county would pay the original purchase price of the five sites, a total of $1,225,654 - minus bond obligations still to be paid - over a 20-year period.

However, action was deferred two weeks to give county staff time to estimate the total cost under the proposed formula.