District government officials and business investors told a Senate subcommittee yesterday that construction of the proposed Washington civic center is vital to the speedy economic redevelopment of the older downtown section of the city.But the Senate subcommittee chairman they were trying to convince said the downtown area is already in the midst of a "building boom."

A polite but reserved Sen. Patrick Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee, questioned Mayor Walter Washington in particular about whether there is still a "great need" for the center and suggested that development of the old downtown east of 15th Street NW would occur with or without such a project.

In contrast to his counterpart in the House, Rep. William Natcher (D-Ky), whose House District Appropriations Subcommittee recently approved a revised center proposal, Leahy continued yesterday to display a skeptical attitude at hearings held to determine the center's fate.

"There's over $400 million in private committed to downtown development, office space is in great shortage and there's a great building boom in Washington now already," said Leahy. "Is the convention center still a great need?"

"I think so," Mayor Washington replied. "In my view, the civic center anchors it (the development) and is what I call a catalyst. It gives you something compatible with the kind of business we have, and that is the tourist industry."

The city's pleas for approval of the center were echoed yesterday by numerous business investors who testified that in one way or another the project would affect their own plans for private development in the city.

Leahy's subcommittee a year ago blocked approval of funds to build the center. Last May, however, the senator engineered a compromise allowing the project to proceed if the city reduced its cost, scaled down its size and secured commitments from the business sector to build privately financed "spin-off" development that would generate enough tax revenues to cover the center's yearly construction and operation costs.

The revised center plans now call for a $99 million project instead of one costing an estimated $116 million, but Leahy has questioned whether the list supplied by the city of spin-off developments is related to the project and firm enough to provide more than $7 million in new tax revenues to help the center break even.

"We seek this assurance so that the taxpayers would not be burdened even more with another scheme that will not pay for itself," said Leahy, who nominally controls the three Democratic votes on the five-member subcommittee and is thus the person to convince if the long-delayed center is to get under way.

Leahy said he had identified 15 of some 49 private development proposals submitted by the city as being the most directly linked to the convention center project and thus likely to qualify as spin-off development.

What Leahy wanted to know from each of the developers yesterday was whether their proposed projects would proceed regardless of the final determination in the convention center controversy.

Several developers, among them A.L. Wheeler, president of the Vega Investment Corp., complained that Leahy was putting them in "a Catch-22" position by requiring that development commitments be firm before the center project had been finally approved.

Wheeler's company wants to build a hotel and restaurant in Georgetown. Wheeler told Leahy "nothing is firm" until financing is arranged, "but getting the civic center makes it easier to come about."

Leahy has scheduled a hearing Thursday for community groups orgainized in opposition to the convention center project, particularly if it is not submitted to a referendum, and he was reluctant yesterday to characterize his reaction to the arguments by business investors.

"If I don't feel the compromise agreement has been fulfilled. I'll vote not to approve," said Leahy, who criticized pro center newspaper editorials.