Carl R. Greene begins each workday as a District government employee by arriving late. Then he goes out for coffee. Sometimes he extends the break into lunch. A quick check back at his office and then he works out at his health club for several hours. Sometimes he doesn't bother to return to work before going home.

Greene, 33, is paid $47,000 a year as an accountant assigned to the office of financial management, headed by Deputy Mayor Robert Pohlman. Since July this self-described workaholic says he has had practically no work to do and that his requests for assignments have been ignored.

"I love to work," Greene said. "The District government is trying to kill me by giving me no work to do."

With a new mayor in office who has pledged to cut the fat from the work force and who faces a $300 million deficit this year, Greene would appear to be a prime candidate for unemployment.

But it was Greene, a computer expert, who called attention to what he considers his pay-for-no-work situation. And Alphonso Jackson, the former head of D.C. public housing who hired Greene in 1988, sings his praises.

"There is no one in the country who knows computers better than Carl," said Jackson, who now heads the housing authority in Dallas. "There is no question he is an expert. I would hire him if he would come to Texas."

Jackson credits Greene with creating an accounting system for the city's 12,000 tenants who live in public housing. He also computerized the records of the Tenant Assistance Program. Both those projects saved the city an estimated $370,000 in 1989 and prompted the government to award Greene an $800 incentive award and a plaque for his outstanding work.

"He is a workaholic," Jackson said. "He must be dying with nothing to do."

Laurie Henderson, an executive assistant to Jackson, worked with Greene on several projects at the D.C. housing office.

"Carl was there early in the morning and late at night," she said. "He was there on weekends. He is the kind of guy who wants to earn his money. Others would sit around and not complain if they had no work."

According to Greene, things began to sour at work after he was passed up for a promotion in the public housing office and then was transferred to the finance office. He said he resented the fact that others had benefited from his housing computer work and he complained about that to superiors.

Valerie Holt, Greene's immediate supervisor at the time he changed jobs and now the acting controller in the finance office, said Greene had requested the transfer. As far as she can tell, Holt said, Greene has been given ample work to do since then and has completed his assignments satisfactorily.

"Mr. Greene joined our staff sometime in the summer," she said. "At that time he was assigned to throughly understand the payroll operation so he could play a role in . . . improving our payroll operation. He accomplished that assignment. Currently we are looking to move him to a supervisory role over two sections."

Greene brushes off Holt's assessment of his duties.

"She asked me to look at a few things and I did it. That's not an assignment. That's a consultation."

Pohlman, the deputy mayor for finance and a holdover from the Barry administration, is one of Dixon's chief advisers on budget issues. He could not be reached for comment yesterday.

Greene said that he is hopeful things will improve with Dixon in office.

"I want her to clean house," he said yesterday. during a two-hour interview. "She says she needs new blood and I agree. She should fire all those mayoral appointees."

In November, Greene filed an informal grievance with Holt concerning his assignment to the office of fiance and requested a transfer back to his old job. Holt replied in December that it was not up to her to transfer him.

Since then he has hired a lawyer, sent letters of complaint to the White House and members of Congress and the D.C. Council and filed a formal complaint with Pohlman.

Greene's office at 410 E St. NW is a large, shabby room at the end of a hallway. Documents unrelated to his job fill a bookcase. The gray metal desk is littered with the morning's newspaper and job announcements.

Most important, there is no computer in his office.

"This is a warehouse they gave me for an office," Greene said. "And they have warehoused me."

Late yesterday, Holt said she may have a solution to Greene's complaint.

"If he wants a pay cut, if he thinks he is overcompensated, we will be glad to reduce his salary," she said.