The Fairfax City police and commonwealth's attorney office are investigating allegations of criminal wrongdoing in the operation of the city treasurer's office during the tenure of former treasurer Frances L. Cox, city officials said yesterday.

The Fairfax mayor and City Council decided in a closed-door session Tuesday night to request the investigation, Mayor Frederick W. Silverthorne said.

Cox, who served as city treasurer 27 years, was defeated for reelection last fall. City councilmen and other officials have attacked her for alleged mismanagement of the treasurer's office. City auditors discovered more than $1.3 million in deposits unaccounted for when Cox left office in December.

Cox has countered that the attacks against her operation of the office are politically motivated. She could not be reached yesterday for comment.

City officials refused to discuss details of the accusations under investigation, but said they were brought to the City Council's attention separate from the problems cited in previous audit reports.

City auditors have accused Cox's office of sloppy bookkeeping and mismanagement of city money in several reports dating as far back as 1966, but this week's action by the council is the first time officials have suggested the problems may have involved anything but bad bookkeeping.

Ray M. Birch, elected to replace Cox last year, resigned in January, less than a month after taking over the $30,000-a-year job, saying the job of clearing up the office's books was too much for him. He said the office accounts were in "deplorable condition." Birch said that after taking office he found $14,929 in checks, cash and coins in desk drawers in the treasurer's office.

Birch said the city treasurer's records were "very much in disarray" when he took over the job. He said incoming checks had not been recorded in the proper ledgers for the last four months of Cox's term.

The council has appointed John W. Coughlan interim treasurer until a new election is held next fall. Commonwealth's Attorney Robert F. Horan Jr. said the investigation is being conducted by the Fairfax City police, who will present their findings to his office.