Arlington County has refused to offer free space to the financially strapped Virginia Employment Commission, despite plans by other Northern Virginia governments to help the unemployed in their areas by providing free space for local employment offices.

Arlington County Board Chairman Stephen H. Detwiler, a Republican, told the Employment Commission the county lacks authority to "donate rent-free space" to the state and therefore cannot help the agency open an office in Arlington.

In refusing the state's request for free space, Arlington cited Dillon's Rule, a legal precept employed by courts in Virginia and many other states that says local governments cannot undertake various actions without specific enabling state legislation.

Democratic state legislators in Arlington, who have long argued in Richmond for repeal of the rule, have expressed anger and bewilderment over the county position.

"I think that it's a tragedy that people in Arlington who need and want to work are denied access to jobs because the Arlington County Board is hiding behind Dillon's Rule," said state Del. Mary A. Marshall, a Democrat who is the senior legislator from Arlington. "Not only are other jurisdictions doing it now, but Arlington has done it in the past; . . . back when Arlington did this, it was Democratically controlled."

"I sure think it's a shame," said another Democratic delegate, Warren G. Stambaugh. "I don't understand how other localities can do it and Arlington can't do it."

"I think that it's appalling that in a time of high employment we don't get the service," said County Board member Ellen M. Bozman, a Democratic-backed independent. "It just is hard to believe."

Arlington's position contrasts with actions of other Virginia governments, including Alexandria and Prince William County, that agreed earlier this year to provide free office space to the commission.

Arlington had donated office space to the commission from November 1972 to June 1981, when federal budget cuts forced the commission to close an office in the county, commission head Ralph G. Cantrell said.

But the County Board, controlled by Republicans, has followed an opinion from the county attorney's office. "There was a lack of authority . . . that would permit the city to give free office space to a group such as the Virginia Employment Commission," said Lawrence D. Tarr, assistant Arlington county attorney. Under Dillon's Rule, state laws imply that the county must impose a substantial charge for office space, Tarr said.

Assistant Virginia Attorney General Robert J. Barry dissented in an informal opinion to Arlington and the commission, saying a token lease of $1 a year would be legal. "Arlington County is the only one (city or county) . . . who brought up the legal obstacle," Barry noted.

"We didn't see any problems at all in allowing them to use space that we had," said Alexandria Deputy City Attorney Michael A. Korb, a view echoed by the Prince William County attorney's office.

Because Arlington refused to donate space to the commission, county residents will have to use commission offices elsewhere. The nearest office is in Old Town Alexandria and the Seven Corners area of Fairfax. Both are to be closed and consolidated into an office in the Merrifield area of Fairfax County, although Alexandria has donated space for an employment office on Mount Vernon Avenue.

The Employment Commission has closed a number of offices because of federal budget cuts, but extra funds allowed the commission to offer to open offices this year if the space would be donated, Cantrell said.

Prince William County has joined Manassas and Manassas Park in offering the commission $17,000, which will be used to set up a new office, Prince William officials said. The commission also has agreed to use some office space in Prince William on a part-time basis, county officials said.

After Arlington decided it could not donate space, it offered a small amount of office space near the Courthouse Metro stop at $2,890 a year, plus $480 for parking, Arlington officials said. The state commission turned down the offer.

The agency needs much more office space to adequately offer placement and unemployment compensation services, Cantrell said.

Unemployment in Northern Virginia was 4.6 percent in June, the latest reporting period, well below the state level of 7.6 percent.

Since last October the agency has arranged job placements for more than 2,900 Northern Virginians, Cantrell said. "We were somewhat disappointed . . . but we will move on and provide services to Arlington residents from the Merrifield location."

That office has been criticized by some Arlington residents as inaccessible for persons who must use public transit.