The Health and Human Services Department yesterday published final rules that will allow non-welfare mothers who should be getting court-ordered child support to seek help from the Internal Revenue Service in collecting delinquent payments.

If state child-support enforcement agencies go along with the program the rules are expected to provide a new weapon for parents whose spouses have pledged in court to make child-support payments but fail to do so.

Before the IRS can swing into action, however, the state child-support enforcement agency must attempt to collect delinquent payments, then detail its unsuccessful efforts in certifying a case to the federal government. There is nothing in the law or the regulations that requires the states to be vigorous in the matter.

A Census Bureau study in 1978, the most recent data available, found that 3.4 million women in the United States were supposed to receive child-support payments. About half received all they were supposed to; another 700,000 received some of what they were supposed to get; about 1 million women received nothing. The total loss can be estimated from the Census data at about $4.3 billion in current dollars, according to Barbara Bergman, associate professor of economics at the University of Maryland.

Under the Tax Code, a delinquent child-support payment will be treated by the IRS as if it were a delinquent tax bill. Letters will be sent, agents will call, assets can be seized. However, no interest or penalty can be charged, according to IRS spokesman Ellen Murphy.

IRS involvement in child-support enforcement in the past has been limited primarily to welfare recipients. Federal and state governments have had an increasingly active program of requiring mothers eligible for Aid to Families with Dependent Children (AFDC) to seek child support from the fathers. Such payments, if properly reported, reduce the AFDC load borne by the taxpayer.

Congress extended authority for the IRS to collect for non-welfare mothers in 1980, and various versions of a regulation have been offered since then.

The final regulation, effective Wednesday, requires a minimum of $750 in delinquent child-support payments to have built up before IRS assistance is sought. An earlier draft version proposed a minimum of $75, but, regulation writers said after discussion with the IRS, that number is "unreasonably low."