Some hard evidence is beginning to accumulate that the recession finally is beginning.

There could be another reversal of the apparent downturn in the economy, as has occurred so often during the expansion that began five years ago this month, but sky-high interest rates and a tightening clamp on credit availability make it far less likely to happen this time, most economists believe.

The advent of the recession appears to be the one thing that will push intrest rates down, though precisely when the peak in rates comes or how lofty it will be, is anybody's guess. The prime lending rate at most major banks hit 20 percent last week, and home mortgage rates are above 15 percent everywhere in the country.

There were even strong signs in the March producer price indexes, released last week by the Labor Department, that a drop in demand for a wide range of industrial goods is having a significant impace on their prices.

"Although little hard data are available on the reaction of the economy to the imposition of credit controls and high interest rates, early reports suggest that the recesion may be under way," economist Alan Greenspan told his clients last week.

In March, the Labor Department reported Friday, the unemployment rate rose to 6.2 percent from Febrauray's 6.0 percent. More importantly in terms of analyzing the current state of the economy, the number of people holding jobs dropped by almost 300,000 during the month.

While the biggest employment drop occurred in construction, which is being crippled by the high cost of borrowing money, the number of factory jobs declined, too. Janet Norwood, commissioner of labor statistics, told a congressional committee, "The index of aggregate weekly hours of production or nonsupervisory workers (which reflects trends in both employment and hours) declined by 0.6 of a point in March . . . aggregate hours declined in almost all of the individual manufacturing industries."

Furthermore, the weekly information on initial claims filed for unemployment insurance show a big jump in the latest week -- 473,000 compared to an average of about 400,000 so far this year -- suggesting layoffs are spreading. According to the monthly figures, about 200,000 more persons were unemployed last month because of layoffs than the 944,000 counted in December.

The drops in employment and the number of hours worked is a sure sign production fell, too. It probably will continue to decline, because there are indications goods are beginning to sell more slowly and that will mean fewer orders going to the factories.

Outside of consturction, the industry hardest hit so far is automobiles. Auto sales plummeted in the final 10 days of March, off 27.8 percent from last year's level. And sales earlier in the month were propped up significantly by special incentives such as direct rebates to buyers from the manufacturer.

Altogether, 13 of 40 domestic car and truck plants will be closed this week and large parts of the remaining factories also will be idle. Well over 200,000 automobile workers are on either temporary or indefinite layoffs.

Most analysts also expect the March figures for housing starts, when they are avalilable later this month, to show a further sharp drop. Starts in February already were far below their levels of early last year. Other statistics from the Commerece Department indicate other types of construction -- office and commercial buildings as well as new plants -- are on the verge of a slump, too.

Lumber and plywood mills, particularly in the Pacific Northwest, have slowed production or in some cases simmply shut down as the demand for lumer has fallen. As housing construction dwindles, the same thing will happen to producers of just about everything that goes into a new house, everything from gypsum wallboard and insulation to toilets, diswashers, carpets and furniture. The slowdown in auto production has the same sort of effect on that industry's suppliers.

Hard as it may be for the public shell-shocked by inflation to believe, some of these drops in demand are beginning to show up in the price indexes.

Producer prices for finished goods continued to climb at nearly a 20 percent annual rate in March, but prices for unprocessed materials, which are highly sensitive to supply and demand shifts, dropped for the first time in 11 months. These materials include such items as cotton, iron and steel scrap, hides and skins, coal, and sand and gravel.

Even with energy prices still rising swiftly, the cost of nonfood crude materials fell 1.4 percent, the sharpest drop since June 1977, the Labor Department said. If energy items are excluded, these prices dropped 4.9 percent.

At the intermediate level, inflation was also running much less strongly than the previous two months. For instance,the cost of materials and components for manufacturing fell 0.3 percent in March compared to a 1.4 percent increase in Februarty and a whopping 3.1 percent jump in January.

Moreover, the worst of the energy price hikes were felt in the first three months of the year and should be tapering shortly, except for the bulge in May and June in gasoline prices stemming from President Carter's new oil import fee.

But the surge in inflation so far this year has left its scars on consumers and business alike. Personal income grew very little in February, the latest figures available, and with the decrease in both employment and hours worked, probably was just as weak last month.

That loss of buying power,coupled with the new restraints the Federal Reserve is attempting to place on consumer lenders, may finally have forced consumers to begin to buy less. February data on consumer expenditures showed that was beginning.

Businesses are still rushing to their banks to borrow money these days, but more because business is poor rather than because it is booming. In some cases, sales revenues are falling, creating the need for more outside cash. Meanwhile, inflation has made carrying inventories more costly. And very high long-term loans from banks instead.

But the Federal Reserve's new voluntary limit on expansion of bank lending is beginning to cause more and more banks to say no to would-be borrowers. That is going to contribute to the economic squeeze every bit as much as high interest rates.

So housing is dying in its tracks. The auto industry is severely depressed. Business investment is sluggish at best, with record interest rate levels certain to keep it that way. Consumer incomes are rising very slowly, and falling after adjustment for inflation.

It all adds up to recession, and the latest figures say it has begun.