As the former Secretary of Transportation tells it, the contract landed on his desk about six months ago after an interagency dispute over its approval. "It was a proposal for two or three hundred thousand dollars to study the advantages of walking to work," William Coleman recalled.

"I said, 'For Chrissake, why spend $300,000 on that?"

The proposal, which he turned down, started him thinking, Coleman said. He asked his staff for a list of service contracts - contracts which provide not pencils or airplanes, but services such as economic analyses, policy studies and engineering operations.

The list Coleman received described 131 outstanding contracts from eight Transportation agencies amounting to $104 million . The Federal Aviation Administration, for example, is paying $1 million to a Falls Church computer firms for "technical support to FAA areas involving communication engineering." George Washington University was listed for $140,746 to study "consumer motivation to use public transit."

There are scores of such contracts outstanding that led Coleman to the obvious question:

With nearly 73,000 civilian employees in the Department of Transportation, who needs outside consultants? Why can't the bureaucracy produce reports on "consumer motivation" and "communication engineering"?

The same question has been asked by skeptical members of Congress about the federal government as a whole. It employs nearly 5 million civilian and military men and women at an annual fringe and payroll cost of $70 billion. Why, then, must it dole out billions every year to produce studies, reports, speeches and the like?

The issue is not a new one. But it has far-reaching implications for a new administration intent on examining federal spending. Contracting, an essential part of agencies' operations, is frequently a haphazard process with little regulation or overnight, and is open to abuse.

Although popular opinion tends to equate the government with masses of entrenched bureaucrats, more than $66 billion annually - one-fifth of the federal budget - is spent through contracts to about 250,000 businesses and institutions. The largest procurement - $48 billion worth - is the Defense Department's.

Few would argue that the government should manufacture its own weapons, but a dispute has raged for years ove what services should be contracted out by various government agencies.

Should a military base laundry be run by a private company or by civil service employee? Should the U.S Geological Survey draw its own maps or contract for them? Should the Food and Drug Administration use its own scientists or nire private laboratories to test products?

The studies Coleman questions are a small part of federal procurement. The government buys every imaginable type of service and there is little uniformity across the agencies as to what is contracted out and what is performed in-house.

Since the Eisenhower administration, government policy has directed that commercial and industrial activity - a term that has as many interpretations as there are federal contract officers - be contracted out unless it can be proven to be more cheaply performed in-house. The reasoning is that government should not compete with private industry for work a contractor might do more efficiently.

Under Nixon and Ford, the Office of Management and Budget aggressively promoted contracting over civil service hiring.

The American Federation of Government Employees (AFGE) claims that services contracts have increased 33 per cent in four years, to $9 billion a year. Other estimates go as high as $30 billion.

The contractors' lobby group, the National Council of Technical Service Industries, says contracting for goods and services was 60 per cent of the federal budget in the middle 1960s and has since declined.

OMB has argued, however, that government does not contract out enough, pointing out that contractors could do military equipment repair, janitorial services, film processing, cafeteria work, and electrical work, among other things.

The most vocal critic of contracting is, predictably, AFGE, the largest federal employees union. "In the long run, contracting is no cheaper," saud Greg Kenefick, the union's spokesman.

"There's a tendency for the contractor to perform services and then jack up the price during the second and third year of the contract," he charged.

Likewise, the House Manpower and Civil Service Subcommittee has found, according to its staff director, Paul Newton, that "contractors cost more. Their wage rates are comparable and you end up paying a profit to the contractor.

The prime motive for contracting out, according to Newton and several other experts, has oftern been to circumvent civil servants hiring ceilings imposed by Congress and OMB in the Nixon-Ford years.

Members of Congress, for the most part, tend to sympathize with the contractors. "There's an emotional reaction on the Hill," Newton said. "They react negatively against an estrenched bureaucracy doing work that could be contracted out to their districts."

The contractors say they are more efficient than government agencies. "We advocate a dollar-by-dollar comparison," said Russell W. Richardson, an aerospace industry executive who speaks for the NCTSI. "We think we can beat them everytime."

"Once government hires people, they never fire them. Then you have a bloated bureaucracy. A contractor goes in, gives a report and leaves. There are no damn taxes to pay to support workers who have nothing to do."

Contracts can be windfalls for freelance writers. The National Aeronautics and Space Administration has signed a contract for a 6,000-word article on the Viking Mars landing program. Sen. William Proxmire (D-Wis.", complained that the $24,000 contract amounted to $4 a word for the writer, who already had a $78,850 NASA contract to write about the Apollo Soyuz project.

Charges of bureaucratic favoritism, congressional intervention and lack of competitive bidding also are problems with contracting. The House Government Operations Committee recently reported that only 36 per cent of the government's more than $4 billion worth of contracts for automated data processing in 1975 was fully competitive.

Newspaper accounts have named defense officials who visit the hunting lodges of weapons contractors. A massive investigation of graphic arts firms contracts here last year has resulted in evidence of widespread bribery and kickbacks in several federal agencies.

Of eight 1975 General Services Administration contracts audited by the General Accounting Office, all eight included improper billings. The $24.4 million contracts, for government equipment such as aircraft test machinery, included charges for hours that were not worked, gasoline and lumber that was not used. One company charged 360 paint brushes for an item that was not painted. Another charged 48 gallons of red paint and 40 gallons of black paint to an item that was painted yellow.

Some waste can be attributed to contracting frenzies in the few months before the end of the fiscal year that contractors call "the buying season."

At the end of the year, program heads find they have money left over, according to Donald Boegehold of the General Accounting Office. "They are told by the head of the agency, 'if you don't spend it this year, then Congress won't give it to you next year.'"

So, in the case of consultants' contracts, agencies pour a flood of "requests for proposals" which are published in the Commerce Business Daily. Contractors submit proposals in response.

With a new administration, the time may be at hand to re-examine the policy and procedures of government contracting, Coleman and others said.

The AFGE has been pushing for oversight legislation. "We're asking for a central repository of information on the justification for contracts and on what the government spends," said Kenefick, the union spokesman."

Coleman sees the possible solution as stricter control by each department head. "Once you find out what you are spending for contracts . . . the next step is to analyze each one," he said. "The Secretary should get a briefing and establish a system to get better review - to make sure they don't get out of hand."