Not long ago housing researchers warned of an N acute shortage of rental housing in the Washington area. Today, try telling that to the managers of the Latrobe, a high-rise apartment building on 15th Street and Rhode Island Avenue NW. In an attempt to fill up the 176-unit building, which has been open for a year and a half, they recently offered a half month's rent credit to tenants who bring in new renters.

"You could say that one has to work a little harder nowadays," said Sally Alkire, regional vice president for the National Corporation for Housing Partnerships, the organization that owns the Latrobe, where a one-bedroom apartment rents for upwards of $460 a month, not including utilities.

The Latrobe situation comes as no surprise to some observers, who estimate that nearly 5 percent -- or about 25,000 -- of the area's apartments are vacant, about twice the rate of a year ago. Many of the vacancies are reported to be in higher-priced buildings.

Industry spokesmen say these vacancies are the result of economic conditions, that the recession has cut into prospective tenants' budgets and has forced developers to loose a flood of unsold condominium units into the rental market. Also, apartment marketers say, economic pinches have caused renters to double up in units to cut costs, thereby reducing overall rental demand in some areas.

"I would think the vacancy rate would be at the 4 to 5 percent mark and climbing," said John O'Neill, executive vice-president of the Apartment and Office Buildings Association of Metropolitan Washington, an organization that says it represents owners of more than 16,000 rental units. O'Neill said the oversupply is serious enough that it has prodded the organization to plan a survey of rental occupancy rates -- something it hasn't done in 10 years.

"There has been a general softening in the market," said Gary Chandler, a researcher for the Bethesda-based housing management firm, Dreyfuss Brothers Inc. "Traffic is down, particularly in your projects that have the higher rents," Chandler added. He said that the 15,000 Dreyfuss units had a 0.9 percent vacancy rate in 1980, compared with a 2.3 percent rate in 1980, and noted that interest in renting has dwindled in recent weeks, particularly for those units that rent for $425 to $575 a month.

"We're having a few merchandising problems," said Manda Hazelett, director of marketing for 16,000 "moderate-to-expensive" apartment units owned or managed by the Charles E. Smith Companies in Northern Virginia and in Washington.

Alexandria housing officials say that their rental occupancy survey indicated that a 0.7 percent vacancy rate that had remained stable for the first three quarters of 1981 had jumped to 1.97 percent by the end of the year. A majority of the vacancies occurred in high-rent buildings, said Mark Looney, researcher for the Alexandria Office of Landlord-Tenant Relations.

The metropolitan area gained more than 11,000 rental units over the past decade -- although the District, Arlington County, Fairfax City and Rockville may have lost rental housing over that time period, according to a new report by the Metropolitan Washington Council of Governments.

At the broad, low-income base of the demand pyramid, however, the situation is different, according to some real estate specialists. Alexandria's Looney said landlords in his area feel that there is "a very critical shortage of low-rent apartments."

Testimony from managers of lower-rent apartments bears out Looney's statement.

"I could rent this building three times over without any problem. It's unbelievable," said Janine Levine, manager of the moderately priced Promenade Apartments in the Adams-Morgan area of Northwest. Rental prices for the 206 units are governed by Washington's rent control statutes and range from $308 for an efficiency apartment to around $410 for a one-bedroom unit. Levine said she has about 25 persons on her waiting list and has turned away many more than that.

Prospective tenants at the moderately priced Commons of McLean garden apartment complex face a three-to-six-month wait to move in. Monthly rents for a one-bedroom unit start at $400.

G. V. Brenneman, the recently-elected president of the Washington Board of Realtors, said the rental market is "selectively soft" in certain "pockets" like Adams-Morgan and Dupont Circle, where large numbers of condominiums have gone unsold and are being offered as rental units.

Brenneman, however, believes the softness in the market is not limited to the high-rent projects. He said several rent-controlled buildings along Connecticut Avenue have vacancies, as evidenced by their "For Rent" signs.

Hazelett, of the Charles E. Smith Companies, attributes much of the decreased demand for luxury apartments to the influx of unsold condominium units into the rental market. "I know a lot of the condominiums have been made to be sold -- and they're renting them just above their overhead," she said. . . . (The market) is saturated with condominiums and rentals now."

O'Neill estimated that between 3,000 and 4,000 condominium units have reverted to rentals in this area in recent months -- in addition to the roughly 30 percent of condo units he says are bought and rented by investors. Also, according to other building association officials, many condominium owners, prompted by new tax laws that allow liberal depreciation deductions, are finding it more beneficial to rent, rather than to sell, their units when they move.

Condominium owners who choose to rent unsold units in the District may establish any base rental price they choose but must seek approval for subsequent rent increases, according to an official from the District of Columbia's rent administrator's office. Authorities in suburban Virginia and Maryland have repealed rent control laws.

Washington-area developers added 11,500 new condiminium units to the area from July 1980 to July 1981, bringing the total number of condo units to almost 95,000, the Council of Governments reported.

To add to the ballooning supply of higher-priced rentals is the high number of houses for rent by owners who cannot sell them in the present tough financing market, said Aaron Dodek, chairman of the Montgomery County Board of Realtors' property management committee. Dodek said the board's most recent real estate listing includes 300 to 400 houses for rent, nearly double the number the same time a year earlier.

Average monthly rental prices for advertised houses, some of which are large, modern and well-situated, range from $500 to $1,000, still substantially lower than many monthly mortgage payments now faced by new buyers.