The District government is distributing more than $1 million to nearly 2,000 low-income public housing tenants as settlement in a class action suit that determined the city had overcharged the tenants for rent.

Residents are picking up their checks at the multipurpose center of the Arthur Cappa public housing development in Southeast. The distribution began late last month.

"It's like Christmas, and we are the Santa Claus helpers," said Johanna Earls, special assistant to the administrator of property managment administration, as she handed out checks last week.

"The checks have been for $52 to $3,927," said Earls. "We've had people get religious, break down and cry and nearly faint. I don't know how many times we've heard 'thank you.' The humility and emotion . . . is touching."

In the heat of emotion, she said, ". . . a lot of people [said] they'd like to give part of their money to Mary Stone as a thank you."

Mary Stone is the Cappa resident on whose behalf the 1982 class action suit was initiated by the Neighborhood Legal Services Program. Stone will go to pick up her $400 repayment check this week.

So far, no strangers have dropped by her apartment in the Cappa development to say thank you. "No one has given me any money," Stone said, laughing.

The money is for repayment of rental overcharges collected from tenants between Feb. 1, 1981, and April 1, 1983, and will go to those tenants who purchased one or more utilities during that period.

The suit contended that the city had overcharged more than one-fourth of its tenants since 1977 by failing to adequately reduce monthly rents for those tenants who pay for their own utilities.

Under federal regulations, the city government is supposed to allow tenants who pay their own gas or electric bills to deduct a certain amount from their monthly rent. But while utility rates had increased dramatically, the city's rent reductions had not.

The District government never disputed the violations and eight months after the lawsuit began, rental rates were adjusted.

"It argued, however, that the tenants had no legal right to make the District government return the overcharges," said Lynn E. Cunningham, a Neighborhood Legal Services lawyer, who along with Joel Polin, a private attorney, represented the tenants.

In the end, the tenants won, although some of them knew nothing about the suit until they received a letter recently, telling them to come pick up a check.

When Virgie Mae Ingram went to the center and saw her green check for $2,600, she nearly fainted.

"I can really use this because I'm not working. I had a stroke and a heart attack in January 1983," said Ingram, whose daughter Sheila was a 1976 silver medal winner in track competition in the Olympics.

"I have to go back to the hospital to get a leg operated on and I want to move into an apartment since I can't walk up and down the steps in the house," she said. "I'm going to send my daughter some money, too, because she's in college."

Not everyone was as lucky as Ingram. Some people walked away disappointed, not finding their names on the list for reimbursement. They were asked to return with their leases.

Also, tenants owing more than $200 will receive letters explaining that the amount of their checks will be minus the amount they owe.

They can contest the findings and have a hearing, or they can accept the report and receive their checks.

A second distribution will occur later, making the total of repayments close to $2 million and the number of recipients may go to as many as 3,800 from 16 public housing projects. The tenants affected by the settlement live in such developments as the Carrollsburg Apartments, Barry Farms, East Capitol Dwellings and Lincoln Heights.