The Fairfax County Board of Supervisors, in a shift of policy that could affect thousands of parents and their children, decided yesterday to open its 52 day care centers for school-aged children to youngsters who live near the centers but attend private or parochial school.

Until now, the county-run day care centers, which are in elementary schools, were open only to children enrolled in those schools. Children in public schools without day care centers, as well as private and parochial school children throughout the county, could not attend the centers.

Under the policy adopted on an 8-to-1 vote by the board, private and parochial school children who live within the boundaries of an elementary school that has a day care program will be able to enroll in those centers on a first-come, first-served basis.

Public school students already enrolled in the centers will not be displaced by the new policy, and their siblings will continue to have priority in admission to the program, county officials said. But new families moving into the neighborhood or families with children too young for school will have to compete with private and parochial school children for spots in the centers.

Under the new policy, children at the 64 public schools without day care programs will still be ineligible for the program. The policy will take effect as soon as there are spots open in the day care centers.

"If a child [who attends private school] is eligible to attend public school [with a day care center], then he should be eligible to attend [a day care program] regardless of" where he attends school, said Supervisor Nancy K. Falck (R-Dranesville), who proposed the new policy.

The lone dissenting vote was cast by Supervisor James M. Scott (D-Providence), who said parents will be outraged if, after planning to enroll their public school children in the day care programs, they find that under the new policy the scarce places have been taken by children from other schools.

"It's going to cause hardship to the families and children who attend the public school system," Scott said.

Fairfax officials estimate a shortage of nearly 3,000 spots in county child day care programs, as elementary school enrollments soar and a growing number of mothers enter the work force.

In other actions yesterday, the board asked the U.S. Justice Department to take District inmates into federal prisons to alleviate crowding at the District's Lorton Reformatory in southern Fairfax County, and called for a consultant's study to evaluate management and security at the state's Camp 30 minimum-security facility in western Fairfax County.

The board held the first public hearing on reappointing School Board members under a new state law that requires such a procedure, but deferred final action on the reappointments until May 19.

After debate, the board also approved a $25,000 grant to supplement the state's community diversion program, which handles nonviolent criminals without imprisonment.

During the board's discussion of Lorton, Chairman John F. Herrity called the prison "a very explosive situation [that] will become more explosive as the summer goes on."