Production at the nation's factories, utilities and mines fell 0.5 percent last month while prices at the producer level declined 0.1 percent, reflecting the strong dollar's role in keeping prices low and eroding domestic output.

The decline in the producer price index for finished goods followed no change in January and a small 0.2 percent rise in December, the Labor Department reported yesterday. For the past 12 months, prices of finished goods at the wholesale level increased 0.7 percent, the lowest increase since prices rose 0.6 percent from December 1982 to December 1983, the Labor Department said.

In a separate report, the Federal Reserve Board said that the nation's industrial production declined 0.5 percent in February following a rise of 0.3 percent in January and an increase of 0.1 percent in December.

Manufacturing production dropped 0.4 percent in February, following a rise of 0.1 percent in January, the Fed said. Mining production declined 2.3 percent in February and utilities' output increased 0.1 percent, the Fed said.

The Fed said that the February decline was partly due to adverse weather. Economists said it also reflected efforts by businesses to reduce inventories, resulting in a cutback in production. The decline was widespread among products and materials, the Fed said.

Economists also said that the continuing strength of the dollar has made imports cheaper than domestic goods and is resulting in a flood of foreign goods into the United States, which is holding back domestic production.

The decline also highlights the trend of a large part of the economy's growth coming from services rather than the goods-producing sector, economists said.

"The recent pattern of small increases in industrial production reflects the fact that growth in final demand has slowed down and business firms are trying to work off excess inventories," said Robert Ortner, Commerce Department chief economist. Ortner also said the industrial production figures reflected "the continuing loss of business to foreign manufacturers."

"The industrial production numbers for February, I think, tend to reflect more of an inventory correction than the strong trade deficit," said Jerry Jasinowski, chief economist for the National Association of Manufacturers.

However, Jasinowski said that between 20 percent and 25 percent of manufacturers' problems are "due to the substitution of foreign goods for domestic goods.

"The devastating trade deficit is finally beginning to show up in the domestic economy," Jasinowski said. "The trade problem is serious enough that it is finally having an effect on domestic production."

Jasinowski said that the slowdown in industrial production is enough to shave one percentage point off of his forecast of 4 percent growth for the first quarter this year.

Ortner, however, said that the recent dropoff in production shouldn't affect the Reagan administration's 4 percent forecast for the year, but growth will be "more and more in services. In broad areas of manufacturing, there's not much growth."

The Fed said that consumer goods output declined 0.6 percent in February as the production of automotive goods declined 1.8 percent. Automobiles were assembled at an annual rate of 8.2 million units last month compared with an 8.6 million unit rate in January.

Meanwhile, the Labor Department said prices received by producers of intermediate goods declined 0.5 percent in February and costs of crude materials declined 1.9 percent. The department said the strength of the dollar makes these goods very expensive abroad, reducing the demand for them.

In addition, the infusion of less expensive foreign goods forces domestic producers to be more price competitive, economists said.

These declines in prices at the producer level, however, have not been fully translated into consumer prices, which are rising at a 4 percent annual rate, because much of the cost increases for consumers have been in services that don't compete with foreign goods, Ortner said.

Prices of consumer foods at the producer level declined 0.1 percent last month following a 0.6 percent decline in January. The index for capital equipment increased 0.5 percent following a 0.4 percent rise in January.

The index for energy declined 2.5 percent, about the same as in January. Indexes for gasoline and home heating oil fell, and costs of natural gas rose after five consecutive months of declines, the Labor Department said.

Prices also rose for fresh and dried vegetables, eggs, soft drinks, and shortening and cooking oils after declining in January, Labor said. Prices rose sharply for fresh fruits, bakery products, breakfast cereals and milled rice. Beef and veal prices declined only about half as much as they did in January, while prices declined for pork and processed fruits and vegetables, Labor said.

The index for finished consumer goods other than foods and energy rose 0.2 percent in February, following a 0.7 percent rise in January. Much of the slowdown in that index was caused by a retrenchment in price increases for passenger cars and light motor trucks. Prices for tobacco products also fell.