"Meet Johnny Arellano," says the large advertisement a local sporting goods store published three weeks ago. There's a picture of a vigorous-looking young man carrying a backpack. "He is our resident authority on bike touring," the ad says. "His next trip: Williamsburg, Va., to Seattle! Right now though, he's busy with cross-country skiing."

Johnny Arellano was an undercover District of Columbia policeman up until last July 1, when a city board declared him partially disabled because of a bad back. Now, in addition to his salesman's salary for the sporting goods store, he collects about $500 a month in disability from the city for his bad back.

Interviewed last week, Arellano said that he doesn't carry backpacks, and that "busy with cross-country skiing," really means he shows ski equipment to customers. He only dreams about taking a long bike trip, someday when his back heals, he says. He draws disability pay "because I'm just trying to get what's mine."

He believes he is now under investigation by the police department's internal affairs division. In the months ahead, he expects to be photographed and followed.

In Washington, according to city finance officials, police surgeons and investigators, the system for police and fire disability retirement has run amok.

Most policemen and firemen here, in contrast to the rest of the country, retire on disability, at enormous cost. Since police investigators have been looking for abuses they have found former officers, retired on disability, working as football coaches, bricklayers, farmers and in other towns as policemen.

The problem is a long-standing one that is receiving considerable attention now - as it seems to do each the a top official exchanges his badge for tax-free medical disability payments for the rest of the life.

City police chief Maurice J. Cullinane, who says he is acting on the advice of doctors, is going out on disability as the result of an old leg injury. Now 45, if he lives to a normal age he will collect more than $1 million in retirement pay even if he takes another job, which he has said he will do.

Cullinane's retirement is just one more. Eighty-two per cent of the 2,200 retired city police officers were classified as disabled, as were 83 percent of the 1,000 retired firemen, according to a city study conducted last January.

These percentages are far in excess of other major cities. Los Angeles, for example, has four regular retirements for every disability. In Detroit the ratio is 7-1; in New York it's 13-1.

One of Mayor Walter E. Washington's budget officers said of the situation here: "It's not a matter of taking advantage of loopholes. The door's wide open."

Of 1970 policemen and firemen who applied to the civilian retirement board for disability pensions last year, only nine were refused.

Trying to find out why this is so elicits a lot of finger-pointing. Dependeing upon who is interviewed, culpability is directed at the retirement board, police surgeons, record-keepers and small group of lawyers and doctors in private practice who have perfected techniques for getting disability retirements.

The cost is staggering. "If the system were stopped right now, with everyone now on retirement living a normal lifespan, the cost of the tax-payers would be between $1 billion and $1.5 billion," said one city budget expert. The necessary money is appropriated on a pay-as-you go basis.

About $55 million, almost one-third of the operating budgets for the police and fire departments, went for pensions in fiscal 1977.

The amount would be less, though still substantial, if there were fewer disabilities and more regular retirements.

A policeman or fireman retiring on disability generally receives two-thirds pay, while one retiring optionally after 20 years receives half pay. The disabled pensioner is not taxed. Unlike other civil servants in the District government, police and firemen can retire at any age after 20 years' service. The average retiree is 45 years old, with 19 years' service.

The benefits are among the best for any big city police and fire department in the country and were established by Congress to aid recruiting in a city where federal lawmen receive about the same benefits. Policemen and firemen here contribute about $14,000 apiece toward their retirement and on the average receive benefits of about $700,000 over a lifetime.

Some city budget officials believe the system is "growing like topsy," and may lead to financial disaster.

Budget officials and police surgeons have for years been livid about the number of disabilities in the system here, but they say changes have been minimal. Seven years ago 97 per cent of all policemen and firemen who retired when out on disabality. In 1972 the top police surgeon, Dr. Robert Dyer, wrote to city officials that the system was out of control.

District of Columbia regulations require a physical examination every two years for disabled officers, and a financial report every year. If the disabling injury heals or if income exceeds 80 percent of the pension in two consecutive years, the pension is supposed to be terminated.

But there have been teasing reports of disabled retired officers doing more strenuous work than they did as policemen, and making a lot of money doint it.

For years, however, no one checked. Cullinane, acting with the mayor's permission, set up a unit in his internal affairs division in the spring of 1976 to look into the situation and do followup work.

That unit now consists of 12 policemen and a firemen who spend most of their time investigating the injuries of men under 50 who retire on disabilities. They travel around the country, taking pictures of supposedly disabled men doing manual tasks.

Last year this unit concluded that 20 officers no longer were suffering from the injuries that retired them, and detailed reports were sent to the Police and Firemen's Retirement and Relief Board for action, according to sources. To date, no action has been taken.

One reliable source close to the investigators said the chairman of the board, Percy Battle, for some reason is keeping the cases from the other six board members. Battle, an official in the city government personnel department, says the board periodically considers investigations of possible abuses, although he says he cannot recall any case where the board found a retiree rehabilitated and cut off his pension.

"If there's any backlog of such cases before the board," Battle said, "I'm not aware of it."

Sorting out the truth of these contradictory reported difficult because almost everything the board does is secret. The meetings are held behind closed doors to keep medical and psychiatric reports about applicants from the public, Battle says. The board will not allow any transcripts of its hearings to be reviewed, nor will it announce its decision on any individual. The board is composed of five city government officials, including a policeman, fireman and doctor, and two citizens all appointed by the mayor.

The internal affairs unit found seven people last year who were exceeding the 80 per cent limit on their income. The board discontinued the pension in five of these cases, Battle said.

The internal affairs section itself now handles the financial checking, and the Police and Fire Clinic handles the physical examinations of disabled retirees. A recently-appointed administrative officer in charge of the physicials, Lt. Carl Alexander, said there was a backlog in processing them and he did not know how extensive it was.

Police surgeons, who are supposed to examine each disability applicant at the Police and Fire Clinic and make a recommendation, are particularly disturbed that the final decision is made by a board predominantly composed of laymen and that, in most cases, the only options for the board are to find the man disabled or not disabled.

"One man retired on disability with a stiff trigger finger, and another one because he got a fishhook in a finger," said one police surgeon. He and some of his colleagues favor percentages of disability.

When there are conflicts between the police surgeon's conclusions and those of the applicant's own doctor, the police physicians will not argue, according to informed sources. One police surgeon explained that if the applicant is turned down by the board and then uses the appeal route to the D.C. Court of Appeals, the police surgeon physician can be tied up in a lengthy legal argument.

"Suppose a man comes in and says he has headaches and they won't go away, and he has a statement from a doctor saying he is disabled - what are you going to do?" said one police surgeon. "We won't challenge him.There's the legal risk, and it's just not worth the hassle."

In the past, board members changed from week to week, but under a 1974 reorganization board members now serve two-year terms. This has helped ease some problems, according to Battle.

The percentage of disability retirements, which peaked at 97 per cent of all those during the year 1970, has been steadily decreasing and was down to about 60 per cent last year. Still, few of those who decide to apply for disability are turned down, according to the board's own figures.

Salesman Arellano, 31, was retired on just 40 per cent of his salary because he had less than 20 years service and there was a question about when his injury (a ruptured disc) occurred.

He says he has no regrets about the sporting goods advertisement. "I'm a salesman and it helps me in my business," he says. His exercise is extremely limited because of the back problem, he says, but he wishes he could dance, bowl and play sports.

"I'm just trying to lead a normal life," Arellano says. "Why shouldn't I?"