The latest chapter is unfolding in the audit of the Fairfax city treasurer's office during the last months of former treasurer Frances L. Cox's tenure--a situation which Cox calls "a Greek tragedy playing itself out."

The Fairfax City Council last week grew impatient for Cox to account for a remaining $60,000 in unclassified deposits made while she was treasurer. The council ordered the current treasurer, John W. Coughlan, to complete the outstanding treasurer's reports and "indemnify him and his staff for any liabilities or claims of other parties against them."

Cox was defeated for reelection last November by Ray M. Birch, who then resigned less than three weeks after he took office in January. Birch said the treasurer's office was in "deplorable condition" and that he had found $1.5 million in discrepancies between bank deposits and treasurer's reports from July to December 1981.

Coughlan, a former accounting professor at Loyola College in Baltimore, was appointed to the Fairfax City treasurer's position after Birch resigned.

After the City Council action last week, Cox said her attorney has written the council, saying that she wants to be relieved of any liability for the outstanding treasurer's reports of last year.

"All the records are scrambled like eggs because so many people have been involved," said Cox, who is running for a Fairfax City Council seat in the May 4 election. "We have arrived at a situation in the city where audits are being politicized. It's a sad situation."

But Fairfax City Councilman Carl J. Hemmer said the council told Coughlan to unscramble the treasurer's reports after repeated delays by Cox.

"We met with Mrs. Cox in January and she agreed that by Jan. 29 she would wrap things up so a transition audit could be completed," Hemmer said. "We thought she had carried it out, but in mid-March the auditor notified us that $1.3 million was still unaccounted for in unclassified deposits. So we met with her again March 22, and gave her two more weeks to complete the work. But April 6, we learned another $60,000 in unclassified deposits was still unaccounted for.

"It's gotten to the point where I simply can't tell the citizens that she is going to finish the work on a certain date."

In recent weeks, Cox has worked with Coughlan, he said, going over photocopies of bank deposits to determine where the money came from. Cox "put in long hours and was generous of her time and effort," Coughlan said.

"The money we're talking about came in and was recorded, but we don't know whether it was for property taxes, parking meter receipts or what," he said. "It is just a matter of figuring out where it came from by looking at deposit slips. That remaining $60,000 is going to be a bunch of checks--$100 here and $200 there."

The council voted 3 to 2, with one abstention, on the resolution ordering Coughlan to complete the treasurer's reports. Supporters of the resolution were Hemmer, John P. Perrin and William M. Calnan; opponents were Mary L. Roper and Glenn L. White. William T. Scott Jr., a declared candidate for treasurer next December, abstained.