The Justice Department filed suit against Fairfax County yesterday contending that the county discriminates against blacks and women in hiring and promotions.

The suit also seeks to prevent the county from receiving its annual $542,500 in federal Law Enforcement Assistance Administration funds and $6.65 million annually in revenue sharing funds and to force repayment of those funds the county has received in the past, which could amount to about $55 million, according to the county's Office of Management and Budget.

The suit, filed in U.S. District Court in Alexandria, backs up a threat to sue made last month by Justic Department officials to the County Board of Supervisors. The board voted to defy an ultimatum that it change its employment practices.

The Justice Department based its charges of discrimination on statistics that show that as of last January, 5.6 percent or 383 of 6,973 county employes were black compared to at least 24 percent of the work force in the Washington area. The figures did not include 14,000 people employed by the county school system.

The Justic Department also said the county has refused to provide information concerning its hiring and promoting practices.

The suit charges that the county used written entry level and promotional tests and other criteria that "have a detrimental impact upon blacks and females" but which are not required to assure successful job performance.

"Fairfax County made every resonable effort and responsible effort to recruit blacks and women," said Board Chairman John F. Herrity (R). "We will not lower our standards and hire incompetent or inefficent people. We're not going to spend our taxpayer's money to do that."

Herrity said he would take the court fight to the U.S. Supreme Court if necessary. "It's about time state and local governments stood up to the bullies in the federal government," he declared, identifying the "bullies" as the Justice Department and the Carter administration.

The supervisors rejected pressure from the Justic Department last month, citing their own affirmative action plan adopted in October 1977. The county's plan called for hiring 129 minority group members to fill 325 jobs durings 1978. A report by the County Civil Service Commission released this week says the county had hired 71 minority group members by the end of September.

The report said 20 county government agencies have a low number of minority employes and may require "special methods" to achieve a better racial balance. Of those agencies, two have no minority employes and another lacks minorities in two of its departments.

"We're not saying they have not taken advantage of opportunities to hire minorities," said Norman Dobyns, chairman of the Civil Service Commission. "We'll be working together with the agencies to bring abut some improvement."

The law enforcement assistance money the Justice Department is seeking to withold has in the past been used to buy equipment for the police and sheriff's departments and the jail.