The Arlington County Board yesterday, after heated debate, failed to appoint anyone to serve the remaining 21 days of Ellen M. Bozman's first term on the county's governing body.

Bozman resigned Tuesday after she learned that her dual membership on the Board and a local Health Center Commission violated a state law dating back to at least 1936. After she resigned both seats, many county observers expected her to be reappointed to fill out her term.

But Vice Chairman John W. Purdy's motion to seat Bozman was defeated by a 2-2 tie vote.

Voting with Purdy to seat Bozman was Board Chairman Joseph S. Wholey. Purdy, Wholey and Bozman have formed the liberal majority on the normally five-member Board. Conservative Board member Dorothy F. Grotos voted with Walter L. Frankland, who led the fight against Bozman's reappointment.

The law Bozman violated according to County Attorney Jerry Emrich, states that local officials cannot hold certain offices simultaneously unless specifically exempted from the law. The Health Center Commission, from which Bozman resigned Nov. 28, is charged with developing nursing homes in Arlington. It is not specifically exempted by law, but a similar group in Manassas is.

Emrich, who found the statute while doing legal research for Bozman, called it "the most technical of technicalities" and urged the Board to reappoint Bozman.

As Bozman sat in the back of the room working on her needlepoint, Frankland explained why he opposed Emrich's advice: "I originally thought the logical thing oto do would be to reappoint Mrs. Bozman, (but there) is a possible conflict of interest here."

Louise Chestnut, a citizen who testified at yesterday's public hearing on the issue, told the Board, "Everyone of you serves on other commissions. If Mrs. Bozman is not permitted to serve out her term, Arlington will be a laughing stock. All of us at one time or another break obscure and forgotten laws."

At one point Purdy, who will be chairman of the Board next year, told Frankland, "I don't know why you wish to cloud the status of this Board except for a very narrow and partisan reason. This is simply an oversight by the General Assembly that has not been corrected yet. You're trying to make it look like Watergate."

Frankland said that no matter how old or unpopular the statute was, it was still the law. He added that he was concerned that Bozman's dual memberships might constitute a conflict of interest.

Grotos, who remained silent during much of the discussion, said, "All of a sudden we're the bad guys. We did not create the problem. What I am trying to do is not to make another mistake."

After the meeting Bozman said she was disappointed but not surprised by the vote. "(Grotos and Frankland) realize this is just a technicality. This is the opening gun of the next campaign," she said.

In November Bozman decisively won re-election as an independent to a second four-year term with the endorsement of the local Democratic Party and the Arlingtonians for a Better County organization. On Tuesday, Sherman Pratt, her unsuccessful opponent who was backed by the Republican Party as well as Frankland and Grotos, filed suit in Arlington Circuit Court challenging her eligibility as a candidate.

Pratt claims that Bozman's dual memberships made her ineligible to run for office. Emrich said that the only qualifications for election are residency, age and voter registration.