Voters in one of West Germany's 10 federal states go to the polls Sunday in a local election that has taken on extraordinary national and even international significance because the survival of Chancellor Helmut Schmidt's coalition government in Bonn could be riding on the outcome.

A victory in the Hesse state elections would give the conservative opposition Christian Democratic Union (CDU) not only control of the state house but, far more importantly would give it a two-thirds majority in the upper house of the Federal Parliament in Bonn, where the states are represented.

This would mean the opposition essentially could stop any piece of government legislation it chose to became Schmidt's water-thin majority in Bonn's lower house could not over-rule the huge upper house opposition bloc.

Although the Christian Democrats have said they would not be obstructionists just for the sake of halting new legislation, it is clear that they could either make the Schmidt administration look ineffective or become a major force in shaping new legislation and policies.

Furthermore, a CDU victory here would probably come mostly at the expense of the small Free Democratic Party (FDP) which has been the indispensable partner of the ruling Social Democrats for the past eight years.

If the Free Democrats disappear politically here as they did in two other state elections in June, the ability of Schmidt to hold together his coalition of Social Democrats and Free Democrats in Bonn will also be severely strained.

While an opposition victory here does not guarantee that the Bonn coalition will fall, it undoubtedly will present the Schmidt government with its worst political crisis and usher in an era of political uncertainty to Western Europe's most powerful country.

Paradoxically, Schmidt remains the most popular and respected political figure in West Germany, with public opinion polls consistently showing him far ahead of CDU national leader Helmut Kohl.

In order for the CDU to gain control in Bonn before the next federal elections in 1980, they must precipitate some kind of unavoidable challenge and win. Few people think that the CDU will put itself in the unpopular position of blocking important public legislation. Experienced observers believe the CDU will simply use the next two years to make the government look ineffective and thus he in a better position to finally achieve the victory that they lost by only 1 percent in the 1976 federal election.

Schmidt's Social Democratic Party has been losing strength steadily in many areas around the country in recent years. In Bonn's federal parliamentary system, local party election losses can eventually pile up to thwart even as respected an international figure as Helmut Schmidt.

Some opinion polls give the current coalition Hesse government of Social Democrats and Free Democrats a tiny edge, but the outcome is essentially too close to call.

Hesse, a state with more than 3 million voters includes the major cities of Frankfurt and Wiesbaden. It has traditionally been a Social Democratic stronghold, to the point where it is sometimes called "Red Hesse" and has been ruled by the Social Democrats alone or in coalition since the end of World War II.

Yet the state has been hit by bank scandals and political corruption to the point where the Christian Democrats actually outpolled the Social Democrats for the first time in the 1974 state election and again in municipal elections in 1977 when the Social Democrats lost the mayor's office here and in Wiesbaden.

Wat keeps the Social Democrats in power here and in Bonn is the small free Democratic Party which in 1974 got 7.4 percent of the vote. That was enough to team up with the SPD's 43.2 percent to defeat the Christian Democrats.

But under German law, a party must get 5 percent of the vote to stay in parliament and the Free Democrats fell below that percentage in June in Hamburg and Lower Saxony.

If they sink below that mark again here Sunday, they will threaten the national survival of their party and thus the coalition in Bonn. Even Schmidt's top aides think the party will at best get 5.4 to 5.8 percent here now.

The Free Democrats have long been the tail that wags the political dog in Bonn, enjoying vast national power because they were so necessary as a partner for the Social Democrats to govern. Four of West Germany's top Cabinet ministers - heading the foreign, economic, interior and agricultural ministries - are Free Democrats.

But the party has been losing its identity with the voters lately and whether Schmidt can continue to vest so much power in a party that seems to represent fewer and fewer people - or whether the party will feel it has no more future linked to the Social Democrats - are the key questions.

A Christian Democratic victory here would be largely a testimonial to the Christian Democratic leader in Hesse, Alfred Dregger, 57, an attractive and articulate rightist politician who has steadily gained followers here over the past 12 years.

A victory by Dregger, who tends to align himself with arch-conservative leader Franz Josef Strauss in Bavaria, would also increase right-wing pressure on Kohl, the national leader who is a moderate conservative.

Thus, if Bonn does get a new government, it might be considerably more conservative than the current one, even though Schmidt is generally viewed as to the right of his own party.

The hopes of the Social Democrats are riding on Hoelger Boerner, 47, a plump jovial politician who took over as governor in the wake of the 1976 scandals and has done a great deal to restore his party's favorable image.