Ontario Premier David Peterson came to Washington yesterday filled with questions for the Reagan administration about a free trade agreement with the United States that his central government sees as a way to avoid U.S. protectionism.

Peterson's skepticism over a U.S.-Canadian free-trade pact, which has the support of the Reagan administration, is of critical importance because Ontario makes more than half of Canada's manufacturered products, and the province's $74 billion two-way trade with the United States is larger than U.S.-Japanese trade.

"We are very vulnerable," Peterson said in an interview.

He said he was "the spokesman for caution" when Prime Minister Brian Mulroney presented the idea of a free-trade agreement to a meeting of provincial premiers in August.

He predicted "a lot more reservations down the pike."

If Peterson's skepticism turns to full-fledged opposition, the free-trade pact likely would be scuttled.

Ontario carries the greatest weight in Canada's federal parliament: One-third of its members come from that province, which is the most populous in the country.

The plan has widespread support within the Reagan administration, and Peterson said he will spend a three-day visit here asking goverment officials and key congressmen what form they see a free trade agreement taking and how they see it working.

Peterson said he also will try to persuade them not "to make superficial moves" by passing protectionist bills that will harm trade relations with Canada whether or not there is a trade pact.

With $120 billion in trade passing between them, the United States and Canada are by far the world's two largest trading partners.

Mulroney announced a month ago that his government will enter into trade negotiations with the United States seeking "the broadest possible package of mutually beneficial reductions in tariff and nontariff barriers between the two countries."

He painted the free-trade pact as a way to guarantee Canada secure access to the U.S. market despite protectionist pressures here.

"This issue is fixating Canada today. I don't think it is more of a hiccup down here," Peterson said.

But he said Mulroney's quick acceptance of a free-trade pact as a way to ensure Canada's access to the United States involved "a leap of faith" that he is not willing to make.

He added that "the debate has been at the level of theology" rather than dealing with the substance and economics of the arrangement.

"I want to see what I'm getting. Ontario has the most to lose," said Peterson, a former businessman, who added that industrialists in his province are split over whether to support a free-trade agreement.

He is especially concerned over whether American laws against subsidies and dumping will continue to apply to Canada after a free-trade pact is signed.

These laws against what the United States considers unfair trade practices are becoming a major threat to imports, and other countries are concerned that Congress keeps expanding the definitions of unfair trade practices.

Peterson pointed to a complaint by the U.S. lumber industry that Canada subsidizes its exports through forest management programs, especially in the western province of British Columbia.

The complaint was thrown out as unfounded by the International Trade Commission in 1983, but now Congress is moving to change the law.

"A subsidy here is whatever the latest legislation says it is," Peterson commented. "You are changing the rules of the game."