Mayor Marion Barry proudly released an audit yesterday showing that the D.C. government completed fiscal 1981 with a surprising $68.3 million surplus, but the mayor's critics on the City Council and Capitol Hill immediately cited the audit as proof that Barry's spending and revenue estimates are not reliable.

The surplus contained in the audit is nearly 10 times the $7 million surplus Barry's administration predicted last July, and a far cry from the $60 million deficit projected 11 months ago, which prompted stiff cutbacks in programs and reductions in city jobs.

"What credibility do you have when you say 'tighten your belts' again?" said City Council Chairman Arrington Dixon.

Dixon described the dramatic swing from a potential $60 million deficit to a $68.3 million surplus during fiscal 1981 as a "$130-million credibility gap" and said Barry could expect to face tough questioning when he defends his latest budget proposal before the council and Congress.

"The credibility of this administration is sinking fast," said council member John A. Wilson, chairman of the committee on finance and revenue. "When they would not allow us [the council] to have financial reports, there had to be a reason. I know the reason now."

One well-placed staff member of a House subcommittee that oversees D.C. affairs said yesterday that the audit will generate additional concern about the accuracy of financial data provided by the city.

"I would think it would tend to make the members [of Congress] a little more cautious about the seriousness of some of the numbers," the aide said.

Another House staff aide agreed that the audit's findings were startling, considering what he called the "gloom and doom" estimates provided to Congress early last year. However, he predicted that some members of Congress would applaud the city for showing a surplus at the same time President Reagan and Congress are wrestling with a massive federal deficit.

The $68.3 million surplus, which city officials said has been used to reduce the city's accumulated debt, resulted from tax revenues exceeding estimates by $51.4 million, spending savings totaling $7.7 million, and several favorable adjustments in accounting procedures.

Wilson said city officials were unable yesterday to say which debts had been paid with the surplus. "I am perplexed," he said.

Carolyn Smith, director of the city's Department of Finance and Revenue, said income, sales and gross receipts tax collections during the fourth quarter of fiscal 1981 were unusually large. Moreover, she said some businesses that year intentionally paid additional D.C. taxes, which can be deducted on the federal tax form, to take advantage of new federal tax breaks.

Although city officials were saying until recently that the surplus would be in the neighborhood of $7 million, Smith said she knew late last October that the city's revenues were running ahead of projections by about $40 million.

However, she insisted that figure was meaningless until it had been adjusted to be brought in line with the city's accounting principles. City Administrator Elijah B. Rogers said yesterday he had no real inkling as to the extent of the surplus until about 10 days ago, when he sat down with the city's private accountants to go through the first version of their audit.

Barry yesterday defended his administration's earlier estimates and disputed charges by some City Council members that he had played tricks with revenue and spending estimates.

"There's no way that the D.C. government can hide numbers . . . and I'm never going to allow anyone who works for me to knowingly mislead anyone," Barry said.

Barry contended the audit, prepared by the private accounting firms of Arthur Andersen & Co. and Lucas, Tucker & Co., would prove to be a plus for the District in its dealings on Capitol Hill.

He noted that most of the criticism surrounding its release has come from his political rivals, including Wilson, council member John L. Ray (D-At Large), and council member Betty Ann Kane (D-At-Large), who all plan to challenge him for election this year.

"Obviously, those persons running for mayor can't praise the mayor," he said. "What they're saying is all political rhetoric. What's important is for the auditor to be satisfied."

Some of the sharpest coments came from Ray, who said city budget officials either were incompetent or intentionally manipulated figures "to make the mayor look good."

Apparently sensitive to criticism that Barry unncessarily put the city through a budgetary wringer last year and borrowed $60 million from the Treasury this month when seemingly there was plenty of money left over, Barry and his aides yesterday downplayed talk of a surplus.

"We don't have a surplus--we had revenues over that which was estimated," Barry said. "You can't have a surplus until you have your entire accumulated debt wiped out."

Until yesterday, Barry's administration and the private accountants had pegged the city's accumulated debt at $388 million. But according to the new audit, that debt was reduced to only $309 million by using the $68.3 million surplus to pay off part of the obligations and by eliminating an additional $9.6 million by changing an accounting procedure.

Until now, the city counted all of its employes' accrued vacation time as a current liability. Under the accounting change, $9.6 million of those funds were reclassified as non-current liabilities and no longer were counted as part of the accumulated debt.