An $8.7 million plan to convert the recently closed Pine Ridge Elementary School in Annandale into offices for Fairfax County police and a computerized command post for county emergency operations,has been given preliminary approval by the county Board of Supervisors.

The move is designed to ease overcrowding in other county office buildings, as well as to cut down on use of rented space. It also reflects an effort, being made throughout the metropolitan area, to find new uses for school buildings left vacant as enrollments shrink.

Officials said that after renovation, Pine Ridge, on Woodburn Road near Rte. 236, will house the county's police administration services and operations support staffs, criminal investigations unit and emergency operations/disaster control center. They said moving the emergency dispatch center there will facilitate the complete computerization of the center.

The plan will ease overcrowding in the Massey Building, in Fairfax City, where the emergency operations center is now located, and in the West Springfield Government Center, where the operations support bureau is housed, according to Thomas M. Davis III, Fairfax supervisor representing the Mason District.

The plan, which received preliminary approval July 11, also will allow the county to move some of its offices out of expensive commercial space it now leases in Fairfax City, he said. The county currently spends a total of about $320,000 a year for leased space.

Davis said residents near the school approve of the plan, under which athletic fields and a meeting room at the school will be retained for public use. He said he expects the fields and the school grounds will be better maintained when the county takes over.

Davis also said he was hopeful that locating the command post at the school will force the county to improve traffic control in the nearby area.

The $8.7 million estimated renovation cost is budgeted in the 1984-88 county Capital Improvement Plan. A meeting is set for this week to give residents a chance to air their views before the proposal comes before the planning commission and the board of supervisors in September for final approval.