A D.C. Department of Corrections budget official who publicly questioned city estimates of potential overspending in his department has been told he is being fired as incompetent for releasing information that city officials say was incorrect, according to D.C. government and Capitol Hill sources.

The reported firing of budget analyst Michael Hagstad, which city officials declined to discuss, followed a story in Sunday's editions of The Washington Post in which Hagstad and other city employes disputed estimates by Mayor Marion Barry that their departments were contributing to about $58 million in overspending by city agencies.

Hagstad is chief of the corrections department's office of budget and data analysis and has been an employe of the agency for 10 years. Barry had said previously that expenditures by the corrections department were contributing to the overspending.

"I check these numbers every day, and we don't show any deficit for this year," Hagstad was quoted as saying. "If they can go and put out numbers without talking to people first and making sense, then I feel free to say somebody must be playing games."

Hagstad was told in a letter Tuesday by George Holland, acting director of corrections, that he had 10 days to appeal his dismissal to City Administrator Elijah B. Rogers, according to the government sources.

In addition, two unidentified city budget officials, who, along with Hagstad, were told Monday by Rogers that they were not empowered to speak to the press about the budget, have been told they will be suspended for two weeks without pay, several sources said.

Hagstad, who declined to talk with a reporter yesterday, has told friends that he is being dismissed because of "inappropriate behavior" and "lack of confidence and misconduct" by giving inaccurate information to the news media.

"He's really distressed about it," said Bernard Demczuk, a former corrections employe and a friend of Hagstad's. Demczuk, who now works as a labor organizer for the American Federation of Government Employees, said Hagstad is planning to appeal the firing but "isn't interested in any publicity and is sorry about the whole thing."

Regarding the substance of the comments by Hagstad and others in the Sunday article, Rogers said, "I don't respond to news stories." He said that there was a potential for overspending and that the mayor was taking steps to eliminate the problem. "You can't have a deficit until the end of the year," he said.

"There is a process for personnel matters," he said. "Everybody has rights. I don't discuss personnel matters. That's confidential information."

According to Jose Gutierrez, D.C. personnel director, employes in Hagstad's category have 10 days to appeal any adverse action to the city administrator, who then has 10 more days to act on the appeal. If the administrator decides the employe is to be fired, the employe is given 30 days' notice. He may appeal to the independent Office of Employee Appeals, and subsequently can challenge the action in court.

According to several accounts, Rogers was visibly angry about the news story during an unscheduled meeting he called on Monday with department officials from Corrections, Human Services and Housing and Economic Development -- the three agencies Barry said were responsible for most of the overspending.

"The roof blew off the place. Everybody had a chance to speak up. Obviously everyone was terribly distressed. It was more cold anger," a source said.

Rogers declined to discuss the purpose of the meeting, but did confirm that the officials were told to refer all media inquiries about the budget to himself, Budget Director Gladys W. Mack or the mayor.

Reports of the firing and the suspensions prompted an inquiry from the House District Committee. The local chapter of the American Civil Liberties Union also expressed interest. In 1977, in response to an ACLU suit involving the corrections and fire departments, a U.S. judge ruled the D.C. government could not threaten or punish employes for speaking to the press.