District housing officials have withdrawn their offer of a city government job for the wife of a new high-ranking public housing manager who made his wife's employment a condition for his acceptance of a $41,308-a-year city post.

Last week, public housing director Sidney Glee said Zirl S. Smith, of the Toledo, Ohio, public housing authority, had accepted the post of deputy to the director, the same position he held in the Toledo authority, after receiving assurances from city officials that his wife would be given a city government job. Smith confirmed at the time that his wife, Diane, had accepted a city post.

At the time, Glee and Smith refused to disclose the job offered Smith's wife or its salary. Yesterday, Glee denied that Mrs. Smith had been offered a city job.

"We have not offered his wife a job in the city government," Glee said, adding that he had told Smith only that "I will do all I can to help her get a job and I hope my efforts will prove fruitful."

Smith sent Glee a Mailgram on Aug. 28 stating that "I hope you don't mind if I don't accept your offer until after Diane has either received an acceptable offer or a letter of assurance that she will beemployed within a reasonable amount of time."

Glee said last week that he later called Smith and told him "that when he came in town (on Sept. 9 for the press conference announcing his appointment) he would be told when Diane would report." Despite Glee's announcement yesterday that no job had been obtained for Mrs. Smith, Smith is scheduled to report here for duty on Oct. 15. He said his understanding is that his wife will have a job.

Private companies often offer to find employment for spouses of high-ranking officials. But city officials said it was contrary to District government policy to give such assurances.

"It is not the policy of this administration to make promises for jobs," said City Administrator Elijah B. Rogers.

Diane Smith said she had no comment. She recently received a master's degree in business administration with specialities in marketing and finance from Bowling Green State University in Bowling Green, Ohio, according to her husband. She is currently unemployed, he said.

Geraldine Boykin, a high-ranking official with the local chapter of the American Federation of State, County and Municipal Employees, said she was unaware of the Smith case. But she added that "given the unemployment rate in the city and the people being laid off from government jobs , I would hope nothing like that would happen in our city government."

Smith's own appointment generated confusion last week after the head of the Toledo housing authority said flatly that Smith had not accepted the Washington job offer.

Smith explained the following day that he and his Toledo boss had kept his departure secret because he was involved in sensitive labor negotiations and did not want to jeopardize his bargaining position.

City housing officials also agreed to two other conditions, Smith said. One was to pay his moving expenses to Washington, and the second was to speed up the use of millions of federal dollars available to modernize public housing projects here.

In addition to naming a new public housing management team last week, Mayor Marion Barry also announced that the city government would spend $61.4 million over the next three years to repair about one-third of the city's 12,000 public housing units.

Glee said the city had not agreed to pay Smith's moving expenses and that the modernization funds "were never part of the negotiations."

Smith said he had insisted on his wife's employment because of the high cost of housing and general living expenses in the District. Under city law, Smith is required to live in the city.

"It's awfully expensive in Washington," said Smith, adding that although his new salary represents a $7,000 raise, the increase was "not significant enough" to allow him to duplicate the standard of living he has in Toledo.