When the marshal of Dodge City, Kan., was here sporting his 10-gallon hat and cowboy boots during a recent do at the Kremlin Palace, he spotted another pair of boots in the mostly Russian audience. There for sure was a soul mate.

Indeed it was. The man he struck up a genial conversation with was Francis J. (Jay) Crawford, attired as usual in a pair of expensive, handtooled cowboy boots, chosen from the many pairs lined up in his room at the Intourist Hotel, where he has lived for two years while waiting for the Soviet bureaucracy to find him a permanent apartment.

There are many stories of Jay Crawford and his life here in Moscow. All of them sketch a profile of a man proud of his American origins, who enjoyed his life and hard work in a land that offers enduring difficulties for resident foreigners.

In the small American business community here, the news that Jay Crawford had been seized by Soviet police Monday night and dragged from his car to a cell in forbidding Lefortovo prison was a stunner. The charge reportedly is smuggling, which carries a 3 to 10-year sentence.

The crude police tactics, dragging the American off as his fiancee, Virgina Olbrish, struggled with the police, are without precedent here - even in a country where foreigners are subject to harassment and intimidation unknown in the west.

"It is very hard to understand. Jay is a 'good ole bou' in the best sense of term," said one American who has known him for most of the two years Crawford has been here as product manager for the International Harvester Co., one of the biggest single American trading partners with the Soviet government.

At 38, Crawford has spent many years outside the United States, although he maintains close family ties and financial interests there, including, according to friends, a farm on the Eastern Shore of Maryland and some horses bred for pleasure riding.

He is one of the thousands of American technicians, engineers, bankers, advertising men and other specialists who live around the world, seeking markets for their companies' products and carrying their Americana with them wherever they go. Of that army, only a few dozen reside here, where the government for many years feared dealing with Western capitalists for the techonolgy that can help its inefficient economy run better.

These companies opened shop here beginning in 1972, when Soviet leader Leonid I. Brezhnev and President Nixon signed a series of agreements on mutual cooperation. The companies came to look around in this alien place - and perhaps make a buck.

One of the most successful has been International Harvester, a fact of no little irony and significance in the present situation. The company had long ties here, dating back to pre-revolutionary times, and maintained contacts through the worst of the Cold War.

"Jay is always conscious that he works for Harvester," said one friend. "He takes this very seriously."

Since 1972, Harvester had landed a series of lucrative contracts for the giant earthmoving and construction equipment so cherished by the Soviets. Just last year, it concluded a $32 million deal for move heavy machinery. Within these contracts have come others - the vital spare parts and service agreements to keep the bib machines chewing away at the forests and tundra of Siberia, building roads, pipelines and housing for a nation rich in raw materials.

Jay Crawford has handled this key part of the business for Harvester for the past two years, and by all accounts, he has been very good at it. "He has always gotten along with the Soviet contacts he has," said one friend. "They always have thought highly of him . . . You could tell it."

"I think the cowboy boots helped.

You know this goes over better with the Russians than the gray suit business types," said another. 'You know, the Russians with their love of cowboy lore like this guy. He is a very sympathetic person."

Crawford, who was born in Maryland but now considers Mobile, Ala., his home, normally dresses in smartly styled conservative business suits - with cowboy boots. "He is a very very careful dresser," said one source.

"You see that immediately when you meet him."

Crawford wears glasses, sports a moustache and keeps his light brown hair short. "He's basically a conservative guy. A southerner. Not a red neck at all. A southerner," mused one source who gave him high marks for his technical compentence at trouble-shooting the problems of the giant machines.

"We were at an exhibit and I remember him standing in front of some Harvester loader that had tires bigger than Jay. He talked and talked about what this machine could do, how much it could move, and all with just one man doing it. He has driven it himself and he knew."

His work has carried him to remote parts of the country, always under careful Soviet supervision.

"It's rare that they let you out like that," commented one competitor. 'But if they have a problem with their machinery, the Soviets get you there."

Crawford was required in his job to explain through translators how the sophisticated machines should be repaired, no small feat in a country whose leaders have struggled for years to encourage even routine maintenance of the tractors and other machines so abused across the country.

A bachelor, Crawford is stocky and fighting to control his weight. He is described as as enthusiastic cook eager to try his hand at anything - "Even a good farm breakfast," according to a friend. In his Intourist digs, he has collected Eastern European wines by the case, according to a friend and enjoy sampling bottles with friends.

In Mobile, Alan Nations, who once worked with Crawford at a construction firm there, described him as "easy to get along with. Just an average guy who likes to go hunting and fishing."

When Harvester opened its office here, the Soviets alloted one large, carefully redecorated apartment to the resident manager, Crawford's boss. The product manager, number two in the small office, was given a hotel room and told to wait for an apartment. Harvester recently recalled its resident manager and Crawford has taken over the job on a temporary basis. He has waited for two years for an apartment of his own, once turning down a Soviet offer to a small apartment because his needs in recent months have changed - he has become engaged to Olbrish and wanted more room than the Soviets were offering.

"He met Virginia - Ginnie - as soon as he arrived," one person recalled. "She's being a real trooper now." The 32-year-old secretary-archivist at the U.S. Embassy refused to receive calls from reporters. Her family is said to live in a suburb of Philadelphia and the couple planned to be married later this year. From time to time they have visited Mobile where Crawford has kept a house.

Friends say that Crawford's mother lives in Maryland and is in poor health.

There is a certain structure to foreigner's social life here and Crawford and his friends occupy a niche just below the senior company representatives, in accordance with their slight-by inferior status on their company's tiny organization charts here. Yet Crawford has many friends - senior representatives and diplomats and members of the embassy's commercial department.

To thrive here, as Crawford seems to have done by his friends accounts, a person is aided by a low-key relaxed manner, which Crawford certainly has. He played an occasional hand of poker "for matchsticks" and he was a frequent churchgoer at the American community's Sunday services in the Embassy snack bar.

As to the allegation of smuggling and the report that it may involve currency irregularities as well, no one knows what to make of these things beyond apprehensively trying to review their own attempts to adhere to the bizzare and complex currency regulations that apply to foreigners - regulations which for the most part are not written down anywhere.

"Everyone has the feeling that this is a signal to the rest," said one source. "It is impossible not to transgress their rules somewhere along the line. They set the rules up that way in the first place. This gives them some leverage.

In the past three years, it has been learned, three other American businessmen residing here have come under pressure from the Soviets, and in two cases the problem was currency irregularities.

In the past, the Soviets have gone without fanfare to the U.S. companies and told them they should withdraw their people. The companies have complied, fearful of a fight that might hurt their chances at more business. No one ever envisioned the Soviet police dragging an American businessman from his car on such charges - or that the American would be Jay Crawford.