The U. S. recession is spilling into Canada, putting tens of thousands out of work in the country's industrial heartland and adding impetus to the Liberal government's attempts to lessen Canada's economic dependence on its neighbor to the South.

Worsening economic conditions, rooted in large measure in the U.S. business slump, loom as a major headache for Prime Minister Pierre Trudeau's administration. Many Canadians are more worried about the threats of unbridled inflation and rising unemployment than the internal political squabbles that have occupied the national stage in recent months.

Unemployment in Canada is high already with 860,000 out of work among a population of 23.7 million. Recent predictions are that the number of jobless will reach 1 million by winter, as the Canadian economy experiences what some say will be its worst year in more than two decades.

If this proves true, the unemployment rate here, now on a par with that of the United States and Britain, would be among the highest in the industrialized countries.

Layoffs in the auto plants -- subsidiaries of the Big Three American car manufacturers -- have accounted for nearly one-third of the 60,000 jobs lost in Canada in the last year.

These developments underscore the increasing sensitivity to the fluctuations of the American business cycle that Canadians have felt since World War II, when the United States replaced Britain as Canada's major commerical partner.

Canada and the U.S. do far more trade than any other two nations. With an economy worth $243 billion a year, Canada sells $36.9 billion in goods and services to the United States, and buys $38.6 billion of American imports. Seventy percent of Canada's exports go to American buyers. Japan, the second-largest buyer of Canadian goods, takes less than 10 percent.

Access to a market 10 times its own size has given Canada one of the world's highest standards of living, bu t it also has imposed risks.

"Living next to the United States," Trudeau once said, "is like sleeping alongside an elephant. No matter how friendly and even-tempered the beast, you are affected by every twitch and grunt."

Since the 1960s, increasing criticism has been heard about the nature and effects of these economic ties from a small but vocal group of Trudeau's more nationalistic countrymen.

Arguing that Canada is little more than an "economy colony" of the United States, they point out that Canada's exports to the American market are made up predominantly of fuels, grains, timber and other raw materials. Being highly sensitive to business-cycle swings, these exports exacerbate this country's dependence on the U.S. economy, they say.

In contrast, Canada is a major importer of American machinery and other equipment, a factor contributing to Canada's $13.8 billion annual deficit on manufactured goods trade.

Canada's exports of raw materials last year accounted for a foreign trade surplus of $3.4 billion. But this was outweighed by Canadian interest and dividend payments on U.S. and other foreign investments, and Canada's overall deficit was $4.2 billion.

Because Canada needs to attaract large amounts of foreign captial to offset its huge external deficit, it hasbeen forced to tie its interest rates to those of the United States. Last winter, this led to an unprecedented surge in interest rates that had many Canadians wondering about the need for such dependence on American economic developments.

Since taking office again last spring, Trudeau's Liberal Party has shown signs that it will launch a major effort to trim back the American presence here. As part of a larger industrial strategy with strong nationalistic overtones, Trudeau wants to expand Canadian ownership of the economy -- particularly in the oil and gas industry, which is 75 percent American-owned. Under current planning low-cost government loans would be given to domestic entrepreneurs to buy assets held by foreign companies.

A key vehicle in the Liberal plans is the Foreign Investment Review Agency, set up in 1974 to screen corporate takeovers by non-Canadians. As now envisioned, the agency will be empowered to assess the performance of foreign multinationals on such matters as the amount of research and development spending they do in Canada. The U.S. auto manufacturers here would be particularly vulnerable to such scrutiny. Last year, they spent less than $4.3 million on research and development here, compared with $323 million spent at home.

This is one reason the Liberal government has pushed Washington to renegotiate certain aspects of a 1965 accord under which Canada and the U.S. ragreed to free trade in automobiles and automotive parts. The pact created thousands of jobs here and doubled the sale of Canadian manufactured products to the U.S.. But during the 15 years the pact has been enforced, Canada has accumulated a $10 billion deficit -- $3 billion in the last year alone -- and Canadians have become increasingly dissatisfied with the current arrangements.

The apparent resurgence of nationalistic spirit represented by Liberal policies is by no means clear-cut, however. Many Canadians, including a large number in Turdeau's party, would prefer to see the Canadian-American economic ties strengthened even further rather than loosened. As a solution to Canada's industrial malaise, they propose a free-trade agreement with the United States, perhaps along the lines of the North American Common Market suggested by figures such as Ronald Reagan, Sen. Edward Kennedy and California Gov. Edmund G. (Jerry) Brown.

Although Canadians as a whole do not seem ready to embrace any such concept in the near future, a steady integration of the two economies seems likely to continue despite the pronationalist bent of the current Trudeau administration.