Fairfax County supervisors narrowly voted to support a $24.8 million school bond referendum request yesterday even though four of the nine board members said they worried that voters might reject it. A $51 million park bond issue request already is on the same June 14 ballot.

A subsequent vote "for the record" unanimously favored the school board's request for a referendum on two bond proposals.

One will ask voters to approve spending of $19.7 million to construct two elementary schools, a center for emotionally distrubed students, a secondary school center for the physically handicapped, and to modernize 16 older schools.

The second will ask for $5.1 million to air condition classrooms in 16 schools.

"Some of us are concerned that we will bring the voters to the choking point," said Lee District Supervisor Joseph Alexander. "We don't want both (bond requests) to go down the drain," he said ib explaining his early vote against the request. Supervisors Warren I. Cikins (D-Mount vernon), Alan H. Magazine (D-Mason) and James M. Scott (D-Providence) initially voted against submitting the referendum to the voters this June.

Both School Board Chairman Rodney F. Page and county school Supt. S. John Davis said they were encouraged and pleased by the Board's action. "Now we have to get a campign going and get it (the bond request) passed," page said.

The supervisors also moved to end the controversy with the school board over surplus school sites. The school board - the members of which are appointed by the County Board - had demanded that the county pay the fair market value of surplus land the schools owned. By a 5-to-4 vote, the supervisors accepted a compromise offered by Magazine under which the county would pay the school board the difference between the original cost of the site and the remaining mortgage.

The park authority is interested in developing the surplus sites. The school board said it would use the money the county paid for the land for school construction and modernization.

Some members of the Board of Supervisors said that the county, having once paid for the land through bonds, should not be asked to pay for the land again. Even after yesterday's vote. Board Chairman John F. Herrity accused the school board of "double dipping" by asking to be paid for the land. And John P. Shacochis (Dranesville) said, "someone should explain why we are paying twice for the same land."

After the discussion one school board could justify giving away surplus sites for nothing and then going to the voters to ask for more money to build needed facilities.

In yesterday's vote the supervisors said the use of the payments - over a 20-year-period - for the surplus school land would not be restricted.Last week, the board asked that any payments - over a 20-year-period - for the surplus school land would not be restricted. Last week, the board asked that any payments be used for community oriented athletic facilities.

In other action, the supervisors authorized the county Commission for Women to set up a countywide task force to look into establishing a shelter for battered women who flee domiestic violence.

The request by the Commission for Women is a result of a public hearing held last December on the problem of battered spouses. At the meeting Col. Richard King, Fairfax County police chief, told the women that police officers answered more than 4,000 calls involving domestic violence last year.

"Recent studies by my staff show we have been experiencing instances of family violence much more often than had been believed," King said.

The shelter will provide a place for women and their children to stay temporarily until their domestic problems can be solved.