Sherman W. Pratt, who was decisively defeated in a bid for election to the Arlington County Board last month, filed suit yesterday challenging the legality of the election of the candidate who defeated him, Ellen M. Bozman.

Pratt, who ran as an independent with Republican endorsement, based his challenge, filed in the county's Circuit Court, on a state law that says local officials cannot hold certain offices simultaneously.

Bozman, an independent who has served on the County Board since 1973 and won re-election last month with endorsements from the Democrats and the Arlingtonians for a Better County organization, has been chairman of the county Health Care Commission since 1975.

Pratt contends that her membership on that commission as well as on the County Board made her negligible to run for re-election.

Pratt's suit, formally called a "contest of election," was termed a "tempest in a teapot" yesterday by various county officials and the two liberals on the County Board who have formed the Board majority along with Bozman.

Bozman and other Board members said they were unaware of the state law about membership in organizations until County Attorney Jerry Emrich brouhgt it to their attention last week.

Bozman immediately resigned from the Health Care Commission, a Board-appointed group charged with developing nursing homes in Arlington. She resigned from the County Board yesterday morning, and the Board voted to hold a public hearing on the matter on Saturday. At that time, it is expected that the Board will appoint Bozman to serve the remaining 21 days of her first term on the Board.

Pratt's challenge deals with her second term, which is to begin Jan. 1.

County Attorney Emrich disputes Pratt's contention that Bozman's dual memberships made her ineligible to run for re-election. He points to court precedents and rulings by the state attorney general, in support of his own position.

"In my mind she's been clearly elected. In almost identical circumstances the courts have ruled that a person holding one office would automatically, without any action on his or her part, vacate the first office if re-elected," Emrich said.

Board Vice Chairman JOhn W. Purdy dismissed Pratt's challenge as "nonsense." Purdy added, "She's removed any possible impediment by resigning the Board and (commission) seats. Besides, the only qualifications for office is that she be a resident and a registered voter."

Bozman said she was confident Pratt's legal challenge would fail. "As I understand it, what Sherm Pratt is essentially saying is that I can't be a member of anything," she said.

But Board member Walter L. Frankland Jr., who along with Board member Dorothy Grotos supported Pratt in the last election, said, "I'm backing (the challenge). It means a difference of a majority on the Board." Grotos was more cautious: "If it's a legitimate suit I would support it," she said.