Cablevision said it would contest the board’s allegations and, if necessary, appeal them in federal court. The regional director’s charges would first be appealed to an N.L.R.B. administrative law judge and then to the agency’s five-member board in Washington, before going to a federal appellate court.

In September, after the communications workers asserted that the Cablevision-sponsored vote was a sham, the mayor’s office issued a statement saying, “Mayor de Blasio continues to stand with C.W.A., and finds these new allegations against Cablevision deeply troubling.” After that vote, Cablevision ran full-page newspaper ads urging Mr. de Blasio to repudiate the union, a strong supporter of the Working Families Party, which worked on behalf of the mayor’s election.

The labor board said the Sept. 10 vote was also illegal because some workers believed they had been spied on as they voted. Clarence Adams, a Cablevision field technician, said that an Honest Ballot official had been sitting close to him and looking at his computer screen as he voted.

Mr. Dolan and the Honest Ballot Association said that the balloting was fair and that individual votes had been kept anonymous.

The labor board’s latest complaint asserts that Mr. Dolan, in his speech to the technicians, threatened to deny them new training and technology if they voted to keep the union. The agency also accused him of illegally promising the workers that he would increase their wages and pay the union to disclaim its interest in representing them. Federal labor law prohibits employers from making threats or offering inducements to pressure workers to vote against a union.

The union argues that Cablevision has been bargaining in bad faith partly because it has not offered the Brooklyn technicians wage parity with the company’s other workers, who have gotten raises of $2 to $9 an hour.

Cablevision officials argue that with the union demanding benefits beyond what nonunion workers get, it would be unfair to nonunion workers to give the unionized Brooklyn technicians extra benefits on top of wage parity.