Housing starts plummeted last month to their lowest level in two years, the Commerce Department reported yesterday, the most serious sign to date that the economy may be slowing down.

The chief economist for the National Association of Homebuilders, Michael Sumichrast, said the decline in housing starts in January to an annual rate of 1.66 million represented "the beginning of a recession" for the housing industry.

Because the industry is the first part of the economy to feel the pinch of higher interest rates and restrictive policies, it often serves as a kind of early-warning system for the rest of the economy.

The Carter administration has predicted slower economic growth this year, but some private economists and the Congressional Budget Office foresee a mild recession.

Part of the sharp decline in new housing construction from December's 2.06 million rate was weather related, housing experts said. About half the drop occurred in the snowbound north central region, with most of the remainder in the West.

The Commerce Department also reported yesterday that personal income in January rose a modest $7.9 billion, after a $17.4 billion gain in November and a $21.8 billion increase in December. Again, some special factors increased the apparent size of the drop.

Yesterday's figures followed a report Thursday by the Federal Reserve Board that industrial production in January rose only 0.1 percent, the smallest amount in a year.

The homebuilders' Sumichrast, taking the dimmest view of the January decline, said it "is real and widespread."

"Only about 25 percent of it was winter-related in the Midwest," he said.

Sumichrast blamed the decline on "the high cost of money and high inflation." He predicts that the rate of starts will fall to an average of 1.7 million units in 1979 and bottom out at a 1.3 million to 1.4 million rate in the first quarter of next year.

President Carter's chief economic adviser, Charles Schultze, said housing dropped "partly because of tight money and partly because of cold weather."

Mortgage money has become much more expensive and hard to get in recent months as the Federal Reserve has forced up interest rates in an effort to slow down the economy. But until yesterday's release of the housing numbers, there was little evidence that the Fed's tight policy was working.

The big reason, experts say, was the introduction, approved by the Fed, last year of a new six-month money market certificate paying savers with at least $10,000 to invest at interest rates higher than that being paid on comparable U.S. Treasury securities. The Fed approved the certificates to ease, but not eliminate, the effect of tight money on housing.

"The housing decline came seven months later because of the certificates," Sumichrast said. "But I am not sure whether they are a blessing or a curse" because of the way they have squeezed thrift institutions' profit margins and pushed mortgage rates higher, he added.

In past periods of high interest rates and tight credit, savings flows to housing lenders usually dried up, and so did mortgage availability. During the 1974-75 recession, the construction industry was especially hard-hit.

Last month, however, $6.66-billion-worth of the money market certificates were issued by the nation's savings and loan association, according to the Federal Home Loan Bank Board (FHLBB).

Altogether, the savings and loans garnered $4 billion in net new savings in January, the second best January ever for the industry. Moreover, Kenneth Biederman, the FHLBB's chief economist, said, "We have not seen any significant drop off in forward commitments to lend. What we are seeing is mostly seasonal."

"The key," Biederman said, "will be in the spring when housing activity normally turns up. If it doesn't, then we're in trouble."

The personal income increase of $7.9 billion -- to an annual rate of $1.815 trillion -- was held down by an increase in the Social Security tax rate, from 6.05 percent to 6.13 percent, paid by both employe and employer.

The taxable wage base for Social Security was also raised, from $17,700 to $22,900, effective last month.That change does not affect most workers until much later in the year, but the Commerce statisticians assume in their calculations that its effect is spread uniformly through the year.

Together the Social Security changes lopped $5 billion off personal income last month, the way the statisticians figured it.

On the other hand, the increase in the federal minimum wage and an expansion of coverage to additional workers raised incomes by about $2 billion. Meanwhile, December personal income was inflated by $5.1 billion in income support payments -- $5.1 billion to the nation's grain farmers. CAPTION: Chart 1, Housing Starts,Decline in new housing construction has been blamed partly on inflation and tight money, partly on cold weather. By Milton Clipper -- The Washington Post; Chart 2, PERSONAL INCOME,Personal income increase of $7.9 billion, to annual rate of $1.815 trillion, was held down by Social Security tax boost. The Washington Post