Last year, Maryland's state government hired two seasoned auditors, set up an office for them in New York City, and gave them the immensely complex job of auditing the tax returns of major out-of-state corporations doing business in Maryland.

The results so far, Maryland officials say, have been dramatic. The Tiny auditing office has already uncovered almost $1.4 million in unpaid corporate income taxes that Maryland would otherwise have lost. The cost of maintaining the New York office, by contrast, has been only $69,108.

Maryland's tax-auditing venture in New York, the headquarters for many of America's biggest corporation, is part of a controversial but continuing drive by the nation's financially pressed state governments as they seek to drum up more tax revenue to help keep pace with the state's spiraling costs.

In addition to moves by individual states like Maryland, a coalition of 19, mainly Western states, is embroiled in a sharply contested court battle against 14 major U.S. corporations over the states' tax-auditing efforts. The dispute is now pending before the U.S. Supreme Court.

The state groupings, known as the Multistate Tax Commission, is seeking the right to audit the books of some of the biggest U.S. corpoations, claiming that American business escape at least $1 billion annually in state taxation.

U.S. Steel Corp. and the 13 other major businesses now represented by former Solicitor General Erwin N. Griswold, are challenging the multistate commission's auditing plans as unconstitutional. Business officials dispute the commission's claims, assert it is acting without congresional authorization, complain that some corporations have been harassed with subpoenas initiated by the multistate tax group and contend that the commission is seeking unfairly to impose "duplicate or multiple taxation" on some businesses.

A three-judge federal panel in New York upheld the constitutionality of the multistate commission last July, and the corporations have appealed the lower-court ruling.The Supreme Court has agreed to hear arguments in its fall term.

Maryland - an associate, but not a regular, member of the multistate commission - is following the court battle closely. Unlike the commission's 19 regular members, associate members do not take part in the group's auditing efforts. Neither Virginia nor the District of Columbia is a member of the multistate commission.

The commission's strategy is to audit a single corporation's records for several states at a time. Eugene F. Corrigan, its executive director, asserted in an interview that many corporations now escape considerable state taxation by improperly attributing much of their income to states that exempt it from taxes or have low tax rates. "They're inconsistent in their position from state to state," he charged. "They don't want the states to get the full picture." The result, he said, is "nowhere income" - income that is not taxed in any state.

The efforts by many states to crack down on alleged corporate tax avoidance have apparently been prompted partly by a rise in public opposition to new tax levies and higher tax rates. This public resistance is the "root reason" for the states' attempts to tighten enforcement of existing tax laws, John Shannon, assistant director for taxation and finance of the U.S. Advisory Commission on Intergovernmental Relations, said in an interview.

During the 1960s, Shannon noted, rising costs led a number of states to adopt income and sales taxes for the first time. Today, however, 45 states have corporate income and sales taxes and 41 have broadly based personal income taxes. To boost revenues further, these states must either increase their taxes rates or take firmer steps to collect taxes already due them under existing rates.

Setting up out-of-state auditing offices - often in New York or Chicago, where many large corporations have their headquarters and keep their books - is one increasingly widespread technique used by state governments to seek broader compliance with their corporate tax laws. These out-of-state offices give state tax auditors readier access to the financial records of out-of-state corporations doing business within their own states' boundaries.

Maryland's openings of a New York auditing office is far from an isolated example.

New York State itself, shaken by its biggest city's fiscal crisis, is moving to open out-of-state auditing offices for the first time. James H. Tully Jr., New York taxation and finance commissioner, says he expects legislative approval to set up a 40-member audit staff in Chicago this year and will push for a Los Angeles office next year. The Chicago office is forecast to bring New York net revenues of $7.7 million in its first year.

Illnois, which has had an auditing office in the New York area for 15 years, has started in the past six months to shift is overall emphasis from focusing primarily on sales tax audits to homing in on corporate income tax returns, according to an Illinois Revenue Department spokesman.

Virginia, which has no out-of-state auditing office, nevertheless began sending auditors on out-of-state trips in 1973 for the first time to audit corporate tax returns. Virginia Tax Commissioner William H. Forst says these auditing trips have quickly become "profitable," bringing Virginia close to $2 million in additional revenue in the last fiscal year.

Not all local governments have followed suit. The District of Columbia, which has been repeatedly criticized in recent years for apparent shortcomings in its tax-collection system, conducts only limited out-of-town audits by sending tax auditors on brief trips, and has never set up an out-of-town audit office.

Maryland Comptroller Louis L. Goldstein noted in an interview that Maryland has already added a third auditor to its New York auditing team and will open a two-man auditing office in Chicago this summer. Maryland's moves, Goldstein said, were patterned on similar steps by other states. Maryland's tax collectors, nevertheless, had also been criticized in a state audit report for conducting too few corporate tax audits.

According to Maryland income tax chief George H. Spriggs, two factors emerged in Maryland's New York audits as the main causes for underpayments of corporte incomes taxes. One was failure by some corporations to report some interest earned on investments through a misinterpretation of recently revised Maryland tax laws. The other was failure by some corporations to report sufficient overall tax liability in Maryland by giving inadequate weight in a tax formula to the value of sales contracts signed in Maryland.

Though tax regulations vary from state to state raising complex legal issues, corporations that do business in more than one state are generally liable for taxes in each such state. Their tax liability is usually based on the proportion of their sales, payroll and property holdings attributable to the states where they do business.

Out-of-state auditing offices are not a new development, though their number is now on the rise, California, regarded as a leader in this field, opened its first out-of-state auditing office in 1946, according to state officials. It now has about 160 sales and corporate income-tax auditors based in New York, Chicago and Houston.

The 10-year-old Multistate Tax Commission has become a focus of controversy primarily because of its attempts in recent years to audit the books of major U.S. corporations.

Corrigan, the commission's executive director, said in an interview that the group's audits in the past five years have turned up about $20 million in unpaid corporate taxes, including $10 million during the current fiscal year. Despite the Supreme Court battle, the commission has obtained access to some business books. Its audits, however, have been limited so far because the commission has only nine auditors on its staff, based in New York and Chicago.

The corporations - which in addition to U.S. Steel include Standard Brands, General Mills, The Procter and Gamble Distributing Co., Bristol Myes Co., Goodyear Tire and Rubber Co., International Harvester Co. and International Telephone & Telegraph Corp. - have responded to the commission's claims with a battery of arguments.

They contend that the Multistate Tax Commission violates three constitutional provisions, including requirement that interstate compacts have congressional consent. They argue that what Corrigan terms "nowhere income" amounts instead to legitimate tax incentives provided for businesses by some state governments. They assert that the commission's interpretations of tax laws would subject some forms of corporate income simultaneously to taxation by more than one state. The multistate commission's actions already "are transforming the interstate taxation system," the corporations warn in a court brief.

William R. Brown, secretary for a committee of the Council of State Chambers of Commerce that represents about 100 major U.S. corporations, disputed Corrigan's claim that businesses are escaping at least $1 billion in state taxes annually, saying, don't think it would amount to anything like as much as they're talking about." While conceding that some tax evasion occurs. Brown argued that such tax violations were more likely to be committed by small, rather than major corporations.

The Multistate Tax Commission has stirred considerable controversy even among the states themselves. Several state have quit the organization in disagreements over its tax policies or the economic consequences of its addicts. Others, like Maryland, are waiting to learn the outcome of the Supreme Court contest before deciding whether that the Multistate Tax Commission could "theoretically" give Maryland a tax-collecting boost, but only if the multistate commission augments its audits of U.S. corporations.