The sheriff of Falls Church has no uniform and no office; he does not carry a gun and has not made an arrest in 17 years. When it runs, he drives a badly rusted 1971 Plymouth.It rarely runs.

The mayor and City Council of Falls Church say the city does not need the services of Sheriff John H. Martin. They say it is wasteful to pay almost $12,000 a year to a sheriff whose only duties are to deliver a few court papers at night. They are not pleased that the sheriff has a full-time job as a steam fitter.

In Virginia, where the office of sheriff has been an institution since 1634, getting rid of a sheriff is not easy. In Falls Church, that requires a citywide referendum and approval by the state General Assembly.

Martin, 57, accustomed to the ignominy of being the only one of 126 Virginia sheriffs with no deputy, works as a steam fitter on commercial construction projects throughout the area.

As sheriff, his duties consist of visiting the city hall basement five afternoons a week to pick up court documents, then going around Falls Church to serve them.

In a typical month last year, according to Martin's records, he served 69 warrants and drove 124 miles. For his services, Martin is paid $11,660 annually. Martin said he works 30 to 40 hours a week. Falls Church Mayor Harold L. Miller said Martin's estimate is "subject to challenge."

"I have severe reservations that it takes 30 hours a week to serve fewer than 20 papers in a town this size," the mayor said. Falls Church has 10,000 residents within its two-square-mile city limits.

The papers that Martin serves could easily be served for less money by the Fairfax County sheriff's office, according to Miller. Falls Church already pays taxes to Fairfax County to support the city's proportionate use of the county's sheriff department.

"The job of Falls Church sheriff is useless. There is no need for it," said an authoritative source in the Fairfax sheriff's department. The county now serves criminal court papers in Falls Church and an arrangement could be made to serve the papers Martin now serves, according to Fairfax Sheriff James D. Swinson.

Falls Church City Manager Harry E. Wells and Mayor Miller agree that it is wasteful for the city to be served by two sheriffs. "In these times of austere budgets," Miller said, "it is time to drop this duplication of services."

Sheriff Martin disagrees.

In an interview in his Falls Church home, which serves as the home base for his sheriff duties, Martin said Falls Church will lose money if it abolishes his job.

"The main squawk has been that I do not work 9 to 5. I do my job when I get best results, in the evening. If I thought the job could be done cheaper by the county, I would give it up," Martin said.

Out of a battered brown briefcase, Martin pulled a letter he received Jan. 19, 1978, from Sheriff Swinson which said it would "cost approximately $30,000 per year" for Swinson's office to assume Martin's duties. Falls Church now pays one-third of Martin's salary; the rest is paid by the state.

Swinson said yesterday, however, that his letter does not mean that Falls Church would have to pay more money to the county if it got rid of its sheriff.

"I am the sheriff of Falls Church, too. They vote for me," Swinson said. "That city would save money if they abolished the office of sheriff."

Complaining about the sheriff in Falls Church is much easier than abolishing his office.

Because the sheriff's position is written into the city charter, the only way to abolish the office is for the City Council to call the citywide referendum and for the General Assembly to approve the result. Mayor Miller said the council is considering the referendum.

Meanwhile, Martin said, Falls Church is receiving excellent service and needs an independently elected sheriff.

"To keep, you know, more or less nonbiased. How would you put it? To keep from getting a council-controlled government," he said.