The chariman of the Federal Reserve Board said yesterday the United States might have to impose a surcharge on imports if inflation worsens at home and the dollar weakens abroad.

Testifying before the congressional Joint Economic Committee, Fed chief G. William Miller said that if the dollar did weaken, he would prefer action to limit imports rather than a move to boost interest ates. He said that could "crunch our economy."

Miller's comments came as Chase Manhattan Bank, the nation's third largest, lowered its prime rate from 11 3/4 percent to 11 1/2 percent. A Chase spokesman said it would be a mistake to interpret the action as a signal that interest rates had peaked. (Story, Page D8.)

Talking to reporters after his testimony, Miller stressed that he did not think an import surcharge would in fact be needed. He said he does not think inflation will get worse or that the dollar will weaken.

But even a hint of an import surcharge is likely to bring howls of anguish from other countries.

In August 1971, President Nixon imposed a temporary 10 percent import surchage in an effort to reduce U.S. imports and to force other nations to agree to a major realignment of currency values, including a devalued dollar. At the same time, because of domestic inflation, he ordered controls on wages and prices.

Miller indicated that higher interest rates would not help the dollar because U.S. rates are already substantially higher than in west Germany and Switzerland, whose currencies have been much stronger than the dollar. Higher interest rates help attract investment funds and thereby can help strengthen a currency.

Only last November, rates were raised for just that reason. A key ingredient in the Carter administration's dollar rescue package was a one-percentage-point increase in the rate the Fed charges on loans to its member banks.

Those higher rates apparently have reduced demand for loans, something Chase Manhattan Bank said in announcing its action on the prime rate yesterday. The prime rate is the rate a bank charges its best customers.

In his appearance yesterday, Miller seemed to agree with the bank. He told Sen. William Proxmire (D-Wis.), who asserted that the higher rates are having little effect, that he believed "they are high enough to do the job" of slowing economic growth.

An import surcharge would be inflationary in that it directly raises the cost customets pay for imported goods. In the present case, a surcharge would discourage buying imports becuase of that higher cost, and thus would help the trade balance.

A drop in the dollar's value also is inflationary, however, since a given cost in, say, German D-Marks, translates into a higher cost in dollars. Miller told the joint committee that the dollar's drop cost U.S. consumers about $15 billion last year.

The 1971 surcharge was in effect from Aug. 17 until Dec. 20. Some imports were exempt and the added duty on others was less than a full 10 percent because of various statutory limitations.

About $500 million was collected before the surcharge was lifted. Thousands of importers challenged Nixon's right to impose it, but ultimately the Supreme Court confirmed that he could legally take such an action. The 1971 actions led to the present system of generally floating exchange rates.

In his exchange with Proxmire, Fed Chairman Miller declared, "I dispute that the monetry restraint has had no bite... Business has managed inventories more prudently because of the cost of carrying them.. throughout the economy, decisions on spending have been attenuated."

"The economy," he concluded, "has been slowing from what it otherwise would be doing."

If inflation accelerated, instead of slowing as Miller and administration economists expect, the chairman also suggested that the Federal Reserve "might have to consider changes in housing finance." Miller said that the new six-month money market certificates, which thrift institutions began offering last year, migh t "have to have caps placed on them."

The certificates, which typically pay savers interest of nearly 10 percent today, are credited with helping maintain savings flows into the thrift institutions and keeping mortgage money available for housing buyers.

Elsewhere on Capitol Hill yesterday, Alfred Kahn, President Carter's chief adviser on inflation, told the House Budget Committee that he had raised the question of credit controls with other administration officials, but has been told such controls are not being considered.

Kahn said he has some "interest in the idea" but he cautioned the committee he was not speaking for the administration. Other administration officials have repeatedly denied financial market rumors that credit controls would be imposed. Kahn said he has been told such controls would discriminate against housing purchasers, as well as buyers of durable goods including automobiles.