The complaint filed with the labor board asserts that statements made by Senator Bob Corker and some state lawmakers amounted to “threats” that swayed the VW workers to vote against the U.A.W. In a stinging defeat for the union, workers at the Chattanooga plant voted 712 to 626 against joining the U.A.W., even though the company did not oppose the unionization effort.

In the days before the vote, several state lawmakers warned that they would block future subsidies to the plant — making it less likely to expand — if the workers voted for the U.A.W.

In a statement, the U.A.W. said the anti-union campaign included “widely disseminated threats by elected officials that state-financed incentives would be withheld if workers exercised their protected right to form a union.”

The union cited a statement that Mr. Corker made on the first day of voting: “I’ve had conversations today and based on those am assured that should the workers vote against the U.A.W., Volkswagen will announce in the coming weeks will that it will manufacture its new midsize S.U.V. here in Chattanooga.”