William H. Simons, who lost his 19-year hold on the presidency of the Washington Teachers Union last Saturday, will ask the U.S. Labor Department for a recount because the winning margin was only four votes.

Simons lost to James D. Ricks, chairman of the Ballou High School science department, by a vote of 1,146 to 1,142 in a special election. A U.S. District Court judge had overturned the union's May 1981 election, won by Simons, because it was not conducted by secret ballot.

Saturday's count was the result of a mail-in vote that was monitored by Labor Department officials. Department officials could not be reached for comment on Simons' intention to seek a recount.

"The vote was so close that there is a great possibility that there could have been an inadvertent error . . . ," Simons said.

If a recount fails to change the outcome, Simons said, he will ask that 17 ballots that were challenged by poll watchers be evaluated by Labor Department officials and tallied if they were cast by eligible voters.

"I don't know why they were challenged," Simons said. "I want to make sure that I leave no stone unturned to make sure that the results of the election are correct."