The District of Columbia government has not improved its system for collecting rents from public housing tenants despite promises three years ago to do so, with the result that the amount of unpaid rents has grown to an estimated $3.3 million, the General Accounting Office reported yesterday.

The GAO, the investigative arm of Congress, said that the D.C. Department of Housing and Community Development has no reliable way to verify or collect the overdue payments and is therefore hampered in its efforts to collect from or evict delinquent tenants.

Tenants who pay bills have received erroneous eviction notices; tenants who have moved are still receiving rent notices, and until late 1980, the city entered into unrealistic repayment agreements, according to the GAO.

One tenant, for instance, agreed to pay off $2,740 in delinquent rents at $5 per month over 45 years, while another was given nearly 33 years to pay off a $3,900 debt, the report says.

The city collected $10.5 million from tenants in its 12,000 public housing units during the 1981 fiscal year. It had a backlog of $3.3 million in uncollected rents as of last October, up $1 million from the previous year, according to city records.

GAO officials said, however, that because of poor record keeping and documentation, the amount of uncollected rents could not be verified.

In addition to the problem with public housing rents, the GAO said yesterday that because of inadequate bookkeeping, the city also has failed to collect about $900,000 from tenants who rented buildings owned by the city's urban renewal authority, the Redevelopment Land Agency.

In 1979, the GAO issued a report criticizing the city's rent collection system and urging improvements. Three years later, GAO concluded, many of the same problems still exist and the city could be losing substantial amounts of money.

"DHCD's failure to collect delinquent rent has decreased public housing and urban renewal rental income and thus increased the need for additional District funding," the report says.

Housing director Robert L. Moore was not available for comment yesterday, and Mayor Marion Barry, who made improved public housing administration one of his campaign commitments in 1978, declined to comment. His press aide said he had not seen the final report.

However the GAO report included a letter from Moore, dated April 8, in which he said that since 1979 the city has used two different private collection firms in an effort to reduce the backlog. Neither has succeeded, both have been terminated and the city is currently looking for another firm, Moore said.

In April 1981, the city instituted an automated system for keeping track of rent payments, but the system has not worked properly and the department now hopes to have a new system in operation by July 1, according to Moore's letter.

Moore wrote that by no later than yesterday, the department would mail out a letter to all tenants with delinquent records asking them to get in touch with project managers if the records were wrong. However, Sandy Robinson, Moore's spokeswoman, said late yesterday that she could not determine whether the letter had been mailed out or whether the new payment tracking system would be in operation July 1.

The GAO said that city officials had estimated a rent payment delinquency rate of 97 percent at Edgewood Terrace in Northeast Washington. But when GAO officials investigated, they found a rate of 37 percent.

City Council member H.R. Crawford (D-Ward 7), who owns the firm that manages the project under contract with the city, said yesterday that the delinquency rate is only "3 to 8 percent."

Project managers at two other locations, Arthur Capper Dwellings in Southeast and Sibley Plaza in Northwest, also were interviewed by GAO investigators but not referred to specifically in the report.

Crawford, a former assistant secretary of the federal Housing and Urban Development in charge of public housing, said part of the city's problem stems from the use of mail collection systems at some sites.

"It's always best to collect rents on-site," he said, adding that mail collections are "time consuming and no one really knows who has paid and who has not."

The GAO recommended that the city set up a new system to keep track of current payments and give top priority to collecting from tenants newly identified as delinquents. Older cases of delinquency should be pursued separately, the GAO said.