The Marc Rich case: US tax collector vs. Swiss secrecy. Scene: An Alpine town where money flows freely

The pretty Swiss lakeside town of Zug is one of the few communities in the world to swim in money. Zug (pop. 22,000), just a short drive from Zurich, is a tax paradise where some 9,000 firms pay their dues. One of them: Marc Rich & Co., a giant commodity dealer and a giant tax problem for the United States.

US authorities charge that Marc Rich & Co. avoided more than $20 million in taxes by selling $345 million in oil to its New York company at a price that caused the US subsidiary to lose $110 million. Needless to say, the Rich company paid a lot less taxes in Zug.

The United States is demanding documents from Marc Rich, and a New York judge , Leonard Sand, has ordered the company to pay a daily fine of $50,000 until the papers are handed over. Marc Rich first refused to turn over the papers, but then gave in. Presumably, the implied threat that the company would be blocked from trading in the US, where an estimated one-quarter of its $10 billion to $15 billion turnover is made, did the trick.

Last week the Swiss federal police unexpectedly moved in and impounded the demanded documents to stop the transfer of ''business secrets'' of third parties to a ''foreign government.'' Apparently, the Swiss are thinking about Marc Rich clients.

(In New York, a federal grand jury's investigation of whether the firm illegally evaded taxes and was acting in good faith in attempting to turn over the papers, was postponed until Sept. 19 so US attorneys had more time to obtain the records from the Swiss. The hearing was orginally scheduled for today.)

US authorities are indignant at the extraordinary length to which Switzerland will go to defend its taxpayers.

Little Zug is just as put out by the lengths to which Uncle Sam will go to get his hands on what Zug thinks does not belong to him. Says Zug finance director Georg Stucky: ''Switzerland does not demand the accounts of Exxon-USA in New York when it suspects that Esso in Zurich has sold gas at exaggerated prices.''

''This is a fight between two tax systems, and why should we just cave in to the Americans.''

Adds a federal tax administration official in Bern: ''We are not defending a particular taxpayer, we are defending a principle.''

When one gets down to the nitty-gritty, the principle is that Switzerland does not recognize tax evasion as a crime, only tax fraud. And only if fraud is involved does Switzerland give legal assistance to foreign countries. The Rich case looks like evasion to the Swiss, if anything, and to the Americans there is a difficulty in seeing the difference.

A diplomatic war between the US and Switzerland is brewing, inspired by a 49 -year-old Belgium-born American who appears to have the Midas touch.

Few Zug inhabitants have seen the mystery man who built up a commodity firm in seven years from a net profit of around $14 million to $200 million. No interviews, no photos, no listed private telephone (but probably unbeknownst to Rich, a helpful central telephone lady if you ring up and ask), frequent car changes to avoid the curious, darkened car windows to avoid the snoopers.

Everyone in Zug, however, knows his mammoth glass office block, which has just been completed near the railway station, and in a way symbolizes that in Zug's world everything is in order.

Says former Zug mayor and prominent citizen Walther Hegglin: ''As long as everything goes well with Marc Rich, it goes well with Zug.'' He paid an estimated $12 million in tax to the town, canton, and federal government in the last released year of 1980.

''He pays very promptly, and we like to have him around,'' said a high official in the Zug finance department.

But so would the Americans.