The nation's biggest banks don't quite own each other, but they come close to it, a voluminous new senate study indicates. The leading banks in America are so closely tied together that they control the biggest blocks of stock in each other's parent holding companies.

For instance, America's second biggest bank in terms of assets. New York's Citibank, is owned by Citicorp. But the Morgan Guaranty Trust Co. is the major "stockvoter" in Citicorp.

So, too, for most of the other mammoth banks in New York. Morgan Guaranty holds - and has the power to vote - more stock in the companies that own Manufacturers Hanover Trust Co. (No. 4 nationally), Chemical Bank (No. 6) and Bankers Trust Co. (No. 7) than any other known investor.

In turn, most of the same New York sister banks - plus the Rockfeller family's Chase Manhattan (No. 3) - control the biggest blocks of stock in J.P. Morgan & Co. the holding company that owns Morgans Guaranty. Citibank, Chase Manhattan, Manufacturers Hanover and Bankers Trust are, in that order, the leading stockholders, and voters, at J.P. Morgan.

The most influential money manager of all the nation's banks although it is only No. 5 in terms of assets, Morgan Guaranty is also the biggest "stockvoter" in Bankamerica Corp., whose Bank of America is No. 1.

"The banks are big happy family," says an aide to the late Sen. Lee Metcalf (D-Mont.) who had headed the Senate Governmental Affairs subcommittee which conducted the detailed staff study over a six-month period.

The study found that the voting rights to stock in large U.S. corporations are concentrated in a relatively few bank trust departments (led by Morgan Guaranty), insurance companies, mutual funds and their related investment advisory companies. Other people are the real owners of most of the stock, but the financial institutions have full authority to buy it and sell it. By and large, the study found, they decide how the shares should be voted.

Entitled "Voting Rights in Major Corporations," the survey disclosed that the power to vote stock in 122 of America's largest corporations - companies so big that the market value of their common stock represents 41 per cent of all outstanding common stock in the United States - is held by just 21 institutional investors. Their voting influence over corporate policy, the report said, "is often augmented by two other powerful levers of control, interlocking directorates and debt-holding."

According to the report, voting power in 56 of the companies, including such corporations as General Motors Corp., Connecticut General Insurance Corp., Middle South Utilities, Citicorp, American Broadcasting Co. Inc., Coca-Cola, American Airlines, Burlington Northern Inc., Shell Oil and American Express Co., is especially concentrated. In 13 of these corporations, family interests control 10 per cent or more of the votes; in another 19, a single institutional investor controls five per cent or more, and in another 24, a combination of five or fewer investors control 10 per cent or more of the votes.

A 235-page companion report by the Congressional Research Service on the actual exercise of voting rights by institutional investors voted doubt of any conscious control of companies in their portfolios, but reported widespread agreement on the ability of big investors to influence corporate policies.

The Senate staff study itself included a corporation-by-corporation listing of all the identifiable major stockholders in the 122 corporations which, with their 2,259 subsidiaries and afifliates, include the biggest insurance, utility and retailing firms in the country.

For General Motors, the report showed the top 34 stockholders, led by the National Bank of Detroit with voting power over 6.21 per cent (17.8 million) of GM's voting shares, and by Morgan Guaranty with 1.13 (5.6 million votes. The top 10 institutions in charge of GM shares, eight of the them banks, control 11.8 percent of the stock in the giant corporation.

"The rapid growth of pension funds is increasing the power of these and other large institutional investors," the reported stated. "Pension fund stock already amounts to 37 per cent of all stock held by all categories of institutional investors, and corporate pension fund assets are expected to double in less than five years and double again by 1986."

Most pension funds, however, are not self-administered. "Management of pension assets, including the authority to buy, sell and vote equities - is concentrated among banks, insurance and investment/investment advisory companies," it continued.

The report, based on holdings at the end of 1976, found that Morgan Guaranty, with $19.3 billion of holdings in stocks and bonds, towered above all other investors. It was "stockvoter No. 1" in 27 of the 122 corporations.

Morgan Guaranty controls 5.2 per cent of the votes in American Express Co.; 7.25 per cent at Connecticut General; 3.26 per cent of Citicorp, and 4.03 per cent of Burlington Northern Inc.

The next dominant investor, the report said, is Citibank, which ranks among the top five stockvoters in 25 corporations.

At the same time, the report emphasized, "the principal stockvoters in large banks are - large banks." Citibank ranks first not only at Morgan Guaranty (with 2.63 per cent of the votes to Chase Manhattan's 1.43 per cent) but also at First Bank System Inc. with 3.32 per cent. A holding company headquartered in Minneapolis, First Bank System, moreover, has an "all-bank lineup of major stockvoters."

In all, the report said, the 21 leading institutional investors included 11 banks, five investment company complexes, four insurance companies and the Kirby family group, which controls the world's largest mutual fund complex (Investors Diversified Services, Inc.) through the Allegheny Corp.

The information was put together primarily from reports required of all major national banks by the Comptroller of the Currency, voluntary submissions by some of the banks regulated by the Federal Reserve system and the Federal Deposit Insurance Corp., insurance company reports to state authorities, and mutual fund an investment company reports to the Securities and Exchange Commission. Debt relationships between corporations and investors remain the biggest mystery because only the Civil Aeronautics Board collects such information, but the Senate study said no new legislation is needed to fill in the gaps.