Czechoslovakia's hard-line Communist leaders are grappling with a seemingly impossible problem: how to extricate their country from a gathering economic crisis without embarking on politically risky reforms.

For the past 13 years, ever since the toppling of Alexander Dubcek's liberal Communist government following a Soviet-led invasion, Czechoslovakia has been ruled on the basis of a simple political formula. Its main elements have consisted of economic prosperity, tough police controls and almost blind obedience to Moscow.

This formula appears to have succeeded, from the government's point of view, in the sense that it produced a decade of relative stability. The Czechoslovaks apparently were prepared to accept political repression as long as their traditionally high living standards continued to rise.

If Dubcek's successors are now worried men, the reason lies not in the threat of any popular explosion on the Polish pattern but in the prospect of long-term economic decline. Their dilemma is that the kind of reforms that could be undertaken to tackle the crisis are precluded for political and ideological reasons. In 1968, Czechoslovak reformers advocated replacing the mechanism of central planning with a free-market system similar to that which has since been adopted in Hungary.

In Czechoslovakia, however, these economic reforms are associated with Dubcek's political heresy of "socialism with a human face." The result is that "reform" itself has become almost a dirty word for present-day Czechoslovak politicians. Instead of attempting reforms, faced with cutbacks in energy supplies from the Soviet Union and an almost zero growth rate, Czechoslovak leaders are attempting to make the existing economic system work better.

Every day the official press carries lengthy exhortations to managers and workers to cut down on waste, save energy, and make extra efforts to meet the targets set by the plan. First signs are that this campaign, which has been gathering momentum during the past six months, is having very limited success.

Outwardly Prague does not seem like a capital beset by economic crisis. Compared with Warsaw or Bucharest, the shops are overflowing with food and consumer goods. Window displays are attractive and people are well-dressed. The city boasts a modern subway system, built with Soviet assistance, which is cheap--admission costs 10 cents--and efficient. But there is also evidence of decay.

While there is plenty to buy in the shops, Prague citizens seem to have sad, sat-upon expressions on their faces, and a lifeless silence pervades the city. The silence is deepest in the winter when snow muffles the sound of traffic and already muted conversations. On the 14th century Charles Bridge across the Vltava River, snowflakes nestle in the folds of the statues blackened by pollution. It is as if they have acquired white cloaks and are gazing down on the modern city from the misty past.

Once described as "the shop window of Central Europe," Czechoslovakia should more properly be compared with Austria and West Germany than to Poland and Romania. Yet some items such as detergents are already in short supply and Czechoslovaks have taken to panic-buying and hoarding.

Prices for gasoline went up 35 percent in October, and more increases are expected in the new year. Czechoslovak light machinery, once internationally renowned, is becoming more and more difficult to sell for hard currency in the West. Imports of Western consumer items, which helped buy political stability in the 1970s, are being cut back.

The suburbs of Prague and other major cities seem run-down. Many factories have a 19th century look about them, symptomatic of the government's failure to modernize the country's industrial base. Street lighting has been reduced to a minimum to conserve electricity. After first glossing over these economic problems, the government now seems eager to draw attention to them. The aim seems to be to persuade ordinary people that they have been living beyond the country's means and that a period of austerity is inevitable.

The shock therapy was applied by the premier, Lubomir Strougal, who spoke of "unprecedented economic difficulties" in a speech to the Communist Party's Central Committee at the end of October. He revealed that, in the key construction sector, productivity was down 1.7 percent over last year, and three out of four building firms had failed to fulfill their plans.

At a time when young Czechoslovak couples wait up to 10 years for an apartment of their own, Strougal said the plan for housing construction would not be fulfilled this year and targets would be reduced by more than 20 percent in 1982.

Despite attempts to streamline the planning system, he said that every other factory failed to draw up its plan in the correct manner. Hard-coal extraction was down over last year's production, as was the grain harvest (15 percent below target).

After reading reports of the speech, a Czechoslovak housewife commented: "It was a big shock for us. We are accustomed to a relatively good life here, but now we're frightened of higher prices and shortages . . . . We expect to feel it in the new year."

The economic consequences of Strougal's remarks were spelled out at another Central Committee meeting that approved scaled-down economic targets for next year and cuts in energy consumption. The planning minister announced that investments would be cut back by 3.3 percent, a decision likely to result in a much lower rate of industrial growth.

In the meantime, Czechoslovaks will make do the way they traditionally have: by earning a little extra on the side. Cheating the state has almost become a national pastime.

When a Western visitor recently asked for a receipt at a gasoline station, the attendant automatically made it out for 80 crowns ($8) above the correct amount, and slyly suggested splitting the difference. Another visitor reported being offered a complex black-market deal to pay his hotel bill in dollars, based on the fact that hard currencies trade illegally at up to 2 1/2 times the official rate.

A Western diplomat here commented: "In my view the Czech national motto should be that there is more than one way to skin a cat."

Unwilling to introduce major economic reforms, the government is attempting to tackle the crisis with what are euphemistically described as "a set of measures to improve the economy." The measures, pioneered in the Soviet Union, include the payment of bonuses to workers who suggest ways of improving on performance of the plan. Emphasis is also placed on better management techniques and attention to quality.

A year after their introduction, however, the set of measures has produced little noticeable improvement.

The Communist Party daily Rude Pravo recently complained that they were being sabotaged by incompetent middle-level managers and Strougal announced that he was "not at all satisfied" with the implementation. He generally is viewed as representing the technocrats in the party, competing for influence with hard-line ideologists such as Vasil Bilak.

A balance between these two factions is maintained by the Communist Party chief, Gustav Husak, who replaced Dubcek in 1969 after recanting the reforms of the Prague Spring.

For many intellectuals who would like to liberalize the system, the Hungarian model seems attractive. After helping the Soviets crush the Hungarian uprising in 1956, party leader Janos Kadar sought to reconcile the population to Communist rule through gradual political and economic relaxation.

This is a course, however, that Husak has never seemed politically strong enough to adopt. The difference between the two leaders is caught by a saying popular in Eastern Europe: "In 1956, Kadar proved himself a good Communist so he later had to show that he was a good Hungarian, too. Husak showed that he was a good Czechoslovak in 1968 and now has to demonstrate that he is a good Communist."

The small human-rights movement is weak and dispirited. Even at a recent peaceful gathering to honor John Lennon on the first anniversary of his death, the police checked the identity cards of participants, apparently in an attempt to make the police presence felt.

The small band of rights activists is isolated from the rest of the population. Some, such as the internationally renowned playwright, Vaclav Havel, are in jail while others have been forced to emigrate. Sixteen dissidents are awaiting trial on charges of hostile subversion.