General Motors Corp. yesterday reduced its dividend rate for the second consecutive year and Chrysler Corp. announced a new program of $300 rebates to help sell cars, as the auto industry reported a 20 percent decline in late October sales.

In an announcement that came after the stock markets were closed, GM said its directors had approved a special year-end dividend of $1.50 a share on common stock -- a dollar a share less than at this time last year.

Noting that GM's performance this year "has been influenced by the overall slowing in the pace of economic growth," Chariman Thomas Murphy and President Elliot Estes said in a statement that the dividend takes into account the current outlook as well as capital needs of the nation's largest industrial corporation.

But analysts said last night that the GM decision would be taken by investors as a sign of recession, even though the company's officers emphasized their belief that normal auto-buying patterns will return in 1980, with a "strengthening economy."

GM's announcement yesterday means that the company's common stock dividend this year will be $5.30 a share compared with $6 in 1978 and a record $6.80 in 1977. In previous quarters this year, GM paid $1 in March, $1.15 plus a special of 50 cents in June and $1.15 in September. In effect, yesterday's announcement indicates a regular dividend of $1.15 plus a special payout of 35 cents, payable Dec. 10 to owners of record Nov. 15.

Wall Street analysts had been forecasting several months ago that GM's full-year dividend would total about $6.60 a share but an earnings statement from the company last week showing third-quarter profits down 96 percent to $22 million compared with the 1978 period was a considerable surprise.

Without a $121 million credit, the result of lowering an estimate of income taxes due for the first nine months, GM would have reported a loss.

Ronald Glantz, an auto industry analyst at Paine Webber in New York, said last night that the GM announcement will "momentarily influence stock prices but it shouldn't cause people to ignore the fact that GM has serious operational problems . . . Ford is worse and Chrysler is in the process of going bankrupt."

At a time with the auto industry is not earning enough money to modernize itself, GM can squeeze its dividends, Ford can borrow money and "Chrysler can't do either," he stated. By backing loan guarantees to keep Chrysler in business, the government is only making the situation worse, Glantz argued.

"The decision to subsidize Chrysler means that in three or four years, Ford will have to go hat-in-hand to Washington . . . the government is giving aid to Chrysler and not collecting tax revenues from what would be the [extra sales of] GM and Ford if Chrysler was shut down . . . it's one of the more foolish economic decisions of the government," the analyst concluded.

Earlier yesterday, in what Chrysler called a first for the auto industry, the ailing company said a $300 special introductory rebate would be given to the first 100,000 buyers of all company vehicles except for the Plymouth Horizon and Dodge Omni, retroactive to Nov. 1.

Calling on its new designated hitter, Chairman Lee Iacoca, to replace baseball announcer Joe Garagiola in television spots for the promotion, Chrysler said the new offer "will stimulate buyer interest in the full line" of cars and trucks.

Chrysler's need to sell vehicles was evident in sales reports from the auto industry yesterday, showing that the nation's third-largest automaker suffered a 56 percent decline in sales to just 18,859 cars for the last third of October. For the month as a whole, Chrysler sales were down 39 percent to 67,689.

Overall, according to the industry data, October sales for the U.S. industry were down by 21 percent to 728-170 from 883,926 in the 1978 period, even though American Motors and Volkswagen posted gains. Importers sold an estimated 171,000 cars, about the same as the last year, bringing total auto industry sales volume to 899,170 -- down 19 percent from a year ago.

For the month, GM was off 22 percent and Ford was down 19 percent. AMC sales rose 37 percent to 17,632 and VW was up 293 percent to 18,935. In part, the weaker October sales were attributed to late introduction of 1980 models.

But in the Oct. 21-31 period, sales continued to be sluggish with GM off 22 percent, Ford down 16 percent and AMC up an estimated 129 percent on the strength of new four-wheel-drive cars and station wagons.

In another development yesterday, Chrysler said its financing subsidiary, Chrysler Financial Corp., had reached final agreement on a one-year, $930 million credit agreement with 195 banks.Additional credit may be added by other banks, and the total package will replace a $1.4 billion credit line that expired.

Chrysler was successful earlier this year in reducing its inventory of unsold cars and trucks from about 80,000 vehicles to less that 25,000, with a $400 rebate program. Apparently, the new rebate will apply only to purchases from dealers that agree to buy an unspecified number of 1980 vehicles from the corporation, for which the Carter administration last week endorsed $1.5 billion of loan guarantees.

Iacocca is to close TV spots for the new rebates with the following statement: " $300 won't convince anyone to buy a car or truck they don't want. But it may convince a lot of people to compare our product. That's all we're asking."