The Northern Virginia Transportation Commission apparently violated a state law by using secret ballots to elect Alexandria City Council member Beverly Beidler as its new chairman, and must repeat the vote in open session, according to an informal legal ruling from the Alexandria city attorney.

Mrs. Beidler won the secret vote of 7-5 last Thursday defeating Alexandria Mayor Frank E. Mann. The only issue was Mrs. Beidler's personal and political opposition to the extension of Interstate Rte. 66 from the Capital Beltway to the Potomac River. Mann supports the highway project.

After Shirley Johnson, a reporter for the Alexandria Gazette, raised the question of legality at the meeting, NVTC Executive Director Irving G. McNayr sought an informal interpretation of Virginia's Freedom of Information Act.

McNayr said Monday that Alexandria City Attorney Cyril D. Calley informed him that the state attorney general ruled in 1974 that public bodies cannot use secret ballots to elect their officers.

McNayr said the ruling apparently means that Arlington County Board member John W. Purdy remains as chairman until NVTC can hold a new election. That may come at a special meeting tentatively scheduled for tonight. The chairmanship of NVTC, the Virginia planning and financial affilitate of the regional Metro transit authority, rotates annually.

Mrs. Beidler would be the first woman to serve as NVTC chairman, a title (instead of chairperson) that is required by state law.

One day before the disputed NVTC vote, U.S. Secretary of Transportation William T. Coleman Jr. authorized the state of Virginia to build a curtailed version of the 6-5 mile road, provided the state agreed also to support a Metrorail route in the 1-66 median.

Fairfax County Supervisor Martha V. Pennino (D-Centreville), an NVTC member and advocate of 1-66, said her constituents would be outraged if she were to support an opponent of the road, however qualified in other ways that person may be.

At this stage of the 1-66 story, Mrs. Beidler responded, "I don't know that I'd have any (further) say in the matter." But she acknowledged that, as an individual, she would continue to oppose 1-66 if the question arose, although as NVTC chairman she would represent whatever position that body took.

Mann said the most recent Alexandria election ended the Council's prior solid opposition to 1-66. He said Mrs. Beidler's election might undermine NVTC's credibility.

Mrs. Pennino said after the voting that she abstained. Other officers elected for 1977 were State Sen. Edward M. Holland (D-Arlington) as vice chairman and Fairfax Supervisor Marie B. Travesky (R-Springfield) as secretary-treasurer.