Having given up hope of getting the Central Intelligence Agency to pay costs incurred by Fairfax City in defending its role in a CIA-engineered burglary, Rep. Joseph L. Fisher (D-Va.) has introduced a bill in Congress that would reimburse the city.

The legislation seeks $41,958 to repay the cost of defending two lawsuits that arose from the February 1971 break-in of a photography shop on Main Street. Three city police officers then assisted CIA agents in unsuccessfully looking for documents that would link the shop owners to antiwar activities.

The break-in did not become known until 1975, when it was mentioned in a Rockefeller Commission report on domestic spying activities of the CIA.

The shop owner then sued the city, which succeeded in getting the photographer's complaints dismissed. But the city said it spent $41,958 in court costs and fees to attorney John Rust Jr.

After city officials repeatedly were refused reimbursement by the CIA and Justice Department, the Northern Virginia city turned to Fisher for help, Tom Welle, city public affairs officer, said.

"Fairfax City responded to the CIA's call for help," Fisher said. "It is unfair that the city's willingness to cooperate with federal officials should leave it with a substantial bill to pay."