The District of Columbia government has no systematic method of keeping track of the estimated 2,000 abused, neglected and abandoned children under its supervision, or the present whereabouts of the youngsters, many of whom are infants.

According to a report released yesterday by the office of the D.C. Auditor, an agency of the D.C. City Council, the city's Department of Human Services (DHS) "simply cannot state one way or the other in any consistent format who it has or how each child is faring while in its care." DHS is responsible for the children's well-being.

Because the District of Columbia leaves children adrift in the system for years, many never are placed in permanent homes, but are moved from place to place and they can be abused and neglected without the city becoming aware of it. When the city does try to locate them, many have disappered without a trace, said Jean Bower, of the D.C. Superior Count office charged with obtaining lawyers for the children.

Audrey Rowe, a high-ranking DHS official, said the report was outdated. Many of the system's shortcomings, identified by the auditor, were corrected several months ago, she said.

The department now has a matter list of all children under its care and probably has a list of the more than 1,000 foster parents who are paid $254 a month to feed and cloth each child under 12 years of age, and $265 a month for a child over 12, Rowe said.

Groups that monitor DHS's care said that while some improvements had been made, the city does not have a list of all children under its care and does not know the whereabouts of all the children.

The city only has a list of children for whom it pays the monthly stipened. That list does not include children living free of charge in foster homes or others in hospitals whose bills are paid by Medicaid, said Bower and officials with FLOC (For Love of Children).

In addition, since the city places almost half the children with private agencies who in turn put the youngsters in homes, the city has only a list of the agency addresses but has no idea where each individual child is living.

"Usable information of children in foster care is non-existent," said Bower.

In addition to the computer list of children receiving city payments, the department also has individual folders on each child. A random sampling of these showed that 20 percent had not been reviewed for more than a year.

Another 70 percent had not been reviewed for more than three months, although the department's own policy calls for a quarterly review, the report said.

For example, one child who had been turned over to the city at birth in 1967 was last checked on in 1973 and then the address given for the child was incorrect.

"There is no indication that any DHS employe has attempted to find out if this child is alive or well for over six years," the report said.

Since the city does not keep current records on the children's whereabouts the govenment often sends out checks to addresses where the children no longer live. It could not be determined how much money is lost in this way, the report said.