District of Columbia Fire Chief Burton W. Johnson has asked the city for a tax-free disability retirement pension based on an old back injury, and will leave the department in any case by March 1 after 35 years of service, informed sources said yesterday.

Johnson, 60, does not want to discuss his injury publicly, a department spokesman said. The spokesman said he understood that a roof had fallen on Johnson during a fire when the chief was a rookie in the fire department but it could not be determined whether Johnson is saying that caused the back injury. When he was promoted to chief in 1973, Johnson passed a physical examination.

If found eligible by a city retirement board, Johnson would collect come $32,000 in tax free pension, which in net terms is more than he makes now.

Washington is unique among major cities in that the great majority of police and firemen who retire do so on disability, rather than regular retirement. Eighty two percent of the 2,200 police retirees and 83 percent of some 1,000 retired firemen have gone out on disability. The substantial difference to the retiree is that the disability pension is tax-free.

Since World War II every D.C. fire chief has retired on disability, including a man forced from office, one who stayed on the force for 10 years after his injury, one who broke a wrist tripping over a fire hose, and another who fell from a ladder while painting his home and never returned to work.

Johnson was examined recently by a neurosurgeon, Dr. F. Donald Cooney, who reported that Johnson suffers from a degenerated disc.

Other physician not familiar with Johnson's case, sais that condition is common among men of 60, the result of years of wear on discs, which serve as shock absorbes in the lower spine.

Johnson has been on sick leave the last two months, and in early January visited the police and fire clinic to ask physicains there to write him up for disability. Doctors there, initially unable to find any serious injury, sent him to Cooney for a recommendation, a common procedure.

Johnson has pain that comes and goes according to a department spokesman, Francis X. Flaherty, who said, "I've been around him when he can hardly stand."

Among the leading contenders within the department to succeed Johnson are assistant chiefs Jefferson Lewis, 52, and John Devine, 46, and deputy chief John Breen, 55.

THere has been speculation that Lewis, who is black, is the front-runner, but the other sources yesterday discounted that.

Johnson was the city's first black fire chief. He was appointed in April 1973, when the city had a white police chief. Some sources close to the city government and City Council believes that a white chief and a black chief for the two forces is politically prudent. If so, that would work against Lewis, who is black, Burtell M. Jefferson, who succeeded Maurice J. Cullinane as police chief last month is black.

Johnson's application for disability retirement is scheduled for consideration at the Feb. 23 meeting of the Police and Firemen's Retirement and Relief Board, a group of seven citizens and city employes appointed by the mayor.

The board, which meets behind closed doors, came under increased scrutiny when Cullinane retired on disability last month. Cullinane, 45, complained of complications from a knee injury suffered 10 years ago.

Many of those who retire on disability go into other jobs. Cullinane told the board he would like to teach school. Johnson, according to Flaherty, is going to take a year-long vacation to the West Coast after he retires.

Other police and fire officers of lesser rank who have retired on disability have been found working in construction, coaching football, or serving as policemen and firemen in other jurisdictions.

In the past, policemen passed over for promotion have simply gone on sick leave and retired on disability, even though they had no trouble passing promotion physivcal examinations.

Critics of the system say the large number of disability retirements are the results of police and fire clinic physicians, and a retirement board that fails to sufficiently challenge applicants.

Physicians and board members claim that most of the injuries presented to them are knee and back problems that cannot be confirmed by medical evidence, but also cannot be denied.

"How can you say a man does not have a backache or a headache," said one police physician. Applicants frequently are able to obtain outside consultants, who use words like "may," "probably," and "possibly" in describibg a patients's condition, and clinic physicians, fearful of a mal-practice suit alleging that they failed to diagnose a problem, will not mount a challenge.

Board members claim they are more discerning now about these "subjective" injuries, and they contend they are reversing the trend toward disability retirements. In the year 1970, about 97 percent of all D.C. police and fire retire went out on disability, while last year the figure fell to just under 60 percent, according to board chairman Percy Battle.

When he was police chief, Cullinane, concerned about the legitimacy of some of the retirees, instituted a special unit in the intenal affairs division to monitor retirees. That unit has found a number od supposedly disabled men doing manual labor, but the board has yet to review any of the cases, even those sent to Battle months ago. After recent publicity on this, city officials said the problem was being corrected.

In addition, two officers from the internal affairs division have recently been appointed to top positions at the clinic, and they have reportedly argued with some men on extended sick leave that they do not have a case for the retirement board.

Some of these rank-and-file men now complain of a double standard, in that they have to wait months to appear before the retirement board while the cases of Cullinane and Johnson seem to be expedited through the system.

Several members of the City Council said yesterday that they believe Johnson has done a very good job in running the city's 1,450-member fire department, which is about 30 percent black.

The Washington Post reported Nov. 3 that both Cullinane and Johnson would be retiring early this year and that filling those vacancies could create a thorny political problem for the mayor, who is still contemplating running for election to a second term.

Washington scored some political points by moving quickly to fill the police chief's post. If the fire chief position is filled by March 1, it could quickly dissolve a potential issue in this year's political campaigns.