Chrysler Corp.'s production workers have approved a new three-year contract with the ailing company, the United Auto Workers union announced yesterday.

On Capitol Hill, however, the company's prospects for federal financial aid continued to weaken as critics denounced the Carter administration's proposed package of $1.5 billion in loan guarantees.

Without "some kind of support coming in sufficient magniture, that company is going to go under," Michigan Gov. William Milliken warned in Senate Banking Committee testimony.

The Republican governor said his state, which houses the largest concentration of Chrysler workers, "is ready to carry its share of the burden" specifically a $150 million package of land purchases, loans and car purchases for use as prizes in the state lottery.

Miliken argued that Chrysler could not survive a bankruptcy and he urged federal aid to prevent an "economic and human disaster." An abrupt halt of paychecks to 80,000 Chrysler workers in his state would create depression-level joblessness and cause "widespread suffering and trauma . . .on these thousands of men, women and children," Milliken said.

Former Commerce secretary Peter Peterson, however, joined other leading business executives in opposing the Chrysler aid proposal. The National Association of Manufacturers and the prestigious Business Roundtable have opposed the aid to Chrysler as has General Motors Corp. Chairman Thomas Murphy.

In prepared testimony, Peterson outlined his own ideas about how the government should supervise the company while keeping it alive with federal loan guarantees. Specifically, he endorsed a review board similar to that which sat in judgment of Lockheed Corp.'s successful resuscitation with loan guarantees earlier in this decade.

But Peterson, now chairman of the New York investment firm of Lehman Brothers Kuhn Loeb, said the Chrysler aid could lead to "ever-rising costs and ever-rising surprises," which he likened to a "Vietnam syndrome."

When pressed by Sen. Donald Stewart (D-Ala.), Peterson said that "reluctantly" he would let Chrysler fail rather than set a precedent for additional corporate bail-outs ". . .As much sympathy as I have for Chrysler and its employes," bankruptcy is a better choice, he declared.

Chrysler's 110,000 UAW workers, who have been voting during the past week, approved a new contract with the company that includes $203 million of delayed and reduced wages and benefits but will cost the firm some $1.3 billion over the three years, according to Alfred Kahn, the administration's chief inflation fighter.