Leasing of Washington office space dropped sharply in 1982, pushing the city's vacancy rate to 9.6 percent at the end of December, not far below the national average of 10.3 percent.

The national figure more than doubles the average of a year earlier, with all of the country's major cities except New York reporting large increases in vacancy rates. The glut is a result of "an office construction boom of historic proportions," according to a report by the commercial leasing firm of Coldwell Banker.

This oversupply of empty offices has led developers to offer generous and sometimes highly imaginative inducements to prospective tenants. According to a story making the rounds in Washington this week, one builder signed a lease with a new tenant after promising free limousine service daily for a year to transport the company's president to his favorite restaurant back in his old neighborhood.

Although Washington's vacancy rate rose dramatically last year, more startling figures were reported in Charlotte, where the rate rose from 1 percent last December to 17.6 percent in March, and dropped back to 15.8 percent by the end of the year. Along with Washington, San Francisco and Houston recorded large increases over their vacancy rates of a year earlier.

In Washington, slightly more than 2.7 million square feet of space was leased last year, a 25 percent drop from the record 3.6 million square feet in 1981, according to a report by the leasing firm of Julien J. Studley Inc.

The biggest drop came in space leased in new buildings--nearly 1.7 million square feet, representing a 46 percent decrease from 1981. At the same time, leasing in existing buildings increased by 118 percent to just over a million square feet of space.

Some of the inducements offered by capital developers include six months of free rent, higher than normal allowances to tenants for finishing and decorating offices and offers by developers to take over the last two or three years of a company's current lease in return for signing a new agreement in a new building. In the last scheme, a developer usually can cut his losses by taking over an old lease under which rent is around $10 a square foot if the tenant signs up for more space at a higher rate in new offices, said Goldstein. The developer expects to sublease the old space to further reduce his costs. Other frequent offers to tenants are options to expand and renew leases, he added.

Average rentals have risen slightly in the last year, from $22.98 per square foot to $23.32 for space in existing buildings, and from $28.88 last year to $29.58 this year for offices in new buildings, according to the Studley report. Goldstein warns, however, that these published figures "do not represent the true rentals for which deals are being negotiated." The true rents are lower in many cases, he added.

The competition for tenants is likely to be even more intense in 1983, with more than 7 million square feet of new space coming onto the market. The total space available for lease this year, in new and old buildings, is expected to reach 13.3 million square feet. At the city's normal absorption rate of about 2 million new square feet annually, this year's space represents a 3 1/2-year supply.

Most of the new construction is concentrated in three areas of the city: The convention center neighborhood, where 2.8 million square feet is being built; the central business district with 2.2 million square feet, and Capitol Hill with 500,000 square feet.

Goldstein said he expects "somewhere between 2 and 2 1/2 million square feet of new space" to be leased this year, up from the 1.7 million leased in 1982. "I think there's the equivalent of a million square feet of tenants" who have been waiting for improvement in the economy and good deals before they leased new space, he said.

In contrast to the District, the Maryland and Northern Virginia suburbs reported the leasing of 4.1 million square feet of office space last year, an 11 percent increase over the previous year. Nearly 2.9 million square feet of the space were in new buildings. Montgomery and Fairfax counties were the leaders in leasing, with 1.2 million and 1.4 million square feet, respectively.