THE DISTRICT government is finding that,

under the administration's new welfare rules, it's not easy for a local government to help the working poor--even with its own money. The federal Health and Human Services Department has warned the District that if it uses local tax funds to restore welfare benefits to working mothers, the department may counteract those efforts so as to make both the mothers and the District worse off than before.

The D.C. Council voted last month to use District funds to maintain welfare benefits paid to low-income families with working mothers. Under changes in federal law made last summer, most of these families would lose all welfare and some would lose Medicaid as well. Others would still get benefits, but in much smaller amounts. If the District makes supplementary welfare payments to families with reduced federal grants, HHS has said it will treat the payments as regular income. This means that a family's welfare benefit would be cut by one dollar for each dollar it gets from the District.

Mayor Barry has suggested to the council-- which will meet again today to decide on a final plan--that one way around the dilemma would be to help working poor families pay their heating and utility bills. By law, energy assistance is not currently counted in determining welfare benefits. The District, however, would have to ask Congress for permission to spend the additional money next year. The administration may also propose cutting off this avenue of help to save money in the 1983 budget. The District could also consider raising its welfare standard and changing its method of computing payments to make up part of the loss to families.

Permanent relief for the working poor will require some action by Congress. The working mothers of the District are not an isolated cause for concern. Members of two House committees-- Ways and Means and Energy and Commerce-- held hearings last month on the effect of the welfare changes on people in Arkansas, Tennessee and Mississippi. The congressmen got a firsthand look at some of the struggling mothers who are now finding that their efforts to help their families--and their honesty in reporting their income to the welfare department--are self-defeating. Some women will lose not only welfare but all medical aid for their children if they work even half-time at the minimum wage.

Last Friday, five members of the Ways and Means Committee introduced a bill that would allow states, at their option, to continue to extend Medicaid coverage to some or all working families previously eligible for welfare. That wouldn't solve the District's problem, but it would be an important first step toward reducing some of the disincentives for work--and for honest reporting of income--that are built into the new welfare policy.