TO LOOK CLOSELY at the case of Francis Crawford, the American International Harvester man who goes on trial in Moscow today, is to be awed by the difficulty in getting the closed Soviet society and the open American society to run in phase.

In New Jersey last May the FBI arrested two Russian non-diplomats for spying. Ordinarily, they would have been quietly packed home - a corner-cutting procedure the United States has found useful over the years to facilitate its own spying and to keep espionage from unduly complicating the Soviet-American scene. The "Woodbridge two," however, were detained and set down for trial in anything but a discreet way.Did the season's Soviet-American sourness have a bit to do with it? More likely, a straight-arrow Justice Department was determined to enforce literally the law.

The KGB, however, was unimpressed. Ignoring considerations of diplomacy and trade, not to speak of justice, it crudely arrested Francis Crawford on a Moscow street, hoked up currency-violation charges and indicated it would swap him for its operatives in New Jersey. As it had to, the United States rejected the deal: An innocent businessman could not be equated with two genuine espionage suspects. So the Russians will try Mr. Crawford. And an American court will try the Russians, starting Sept. 12.

If Moscow is of a mind to remove some of the "grit" that has clogged the diplomatic process in recent months, it will dispose of the Crawford case expeditiously and let the fellow go home. Any other outcome will suggest a truly disturbing degree of KGB control over Soviet policy. Even so, the damage is considerable.

As a result of the Crawford case, the KGB has shaken the American business community, one of the most detente-minded constituencies in this country, and given a number of firms further reason to consider closing their expensive, unproductive offices in Moscow. (We note with dismay, by the way, reports that, while many Moscow-based U.S. firms finally expressed solidarity with Mr. Crawford, some took advantage of International Harvester's misfortune.)

In the coincidental (and unfinished) American debate over trading with Moscow, the Crawford case has strengthened the hand of those who believe that trade is risky, that trade should be used for political retaliation, and that in certain high-technology areas like oil drilling, the United States should sell the service but not the technology itself. For all that the lagging Soviet economy can thank the KGB.

Further, to an American public already troubled by Soviet policy on human rights, Africa and armsbuilding, the case has conveyed that a broad-scale Soviet campaign against detente is on.

We would not contend that the United States has made no contribution of its own to the accumulation of "grit" since last spring. Nor would we deny that the Soviet government has sought recently to remove some of it - for instance, by finally backing off from a full assault on the American correspondents accused of slander. Moscow would do well to back off on Francis Crawford as well. At the point the two countries should not be manufacturing obstacles to their quest for a fair agreement on limiting strategic arms.