Financially troubled Chrysler Corp., which Tuesday reported a record loss of $207.1 million for its second quarter, announced today that it will omit the 10-cent-a-share dividend on its common stock for the third quarter.

But the company's board of directors voted to continue to pay 68.75 cents a share on the preferred stock Chrysler sold last year to raise more than $230 million for the cash-short company.

The nation's third biggest automaker has been hurt by declining sales of its big cars and light trucks and vans as well as heavy expenses involved in redesigning its cars to meet the mileage standards set down by Congress in 1975.

The $207 million second-quarter loss is larger than the $204 million loss Chrysler posted for all of 1978.

The omission of its third-quarter dividend will do little to help the company's plight. At 10 cents a share, dividend payments for the third quarter would have been roughly $6.4 million on the 63.6 million shares of Chrysler common stock outstanding.

Trading in Chrysler stock was halted pending announcement of the board's decision. However, stock investors had anticipated that Chrysler would cancel its dividend and, when trading resumed around 1 p.m., the price of Chrysler stock stayed the same, about $8 a share. However, it was about 12 1/2 cents below Wednesday's close Chrysler ended the day, however, at 7 7/8, down 1/4 from its close on Wednesday.

The big loss announced by Chrysler on tuesday prompted the nation's two most important investment rating services -- Moody's and Standard & Poor's -- to lower the grade of both Chrysler bond issues and the commercial paper issued by Chrysler's financial subsidiary.

As a result, the financial subsidiary -- which uses the proceeds of its commercial paper sales to finance customer purchases of Chrysler cars and trucks -- has had difficulty selling commercial paper. Commercial paper is essentially a corporate IOU issued by a company that needs cash and purchased by a company with spare cash to invest.

Most lines of commercial paper, including Chrysler Financial's are backed by lines of credit with a bank. If the issuing company finds it cannot sell paper to supply the cash it needs to pay off maturing commercial paper, it usually taps its bank for a loan.

Commercial paper matures within 90 days, and much of it matures in a much shorter time, often a week.

Government agencies are monitoring the commercial paper market carefully, sources said.

When Penn Central Railroad went bankrupt in 1970, it couldn't sell any more commercial paper and was forced to go to banks to draw on its lines of credit. That bankruptcy threw the commercial paper market into distress, and many small, but otherwise sound, companies found that they also couldn't sell their commercial paper.

The Federal Reserve System opened wide its borrowing window to permit banks to come up with the funds needed to make good on the lines of credit that back up commercial paper sales.

Because Chrysler Corp. is virtually precluded from raising money by issuing new debt securities, the auto company itself will have to rely heavily on lines of credit it has with banks. The auto company also has aked the federal government for $1 billion in aid over the next two years to help it to underwrite the research and development work necessary to improve mileage on its automobiles.