The nation's Roman Catholic bishops have asked the Supreme Court to reject a private group's demand for church records in the group's legal challenge to the church's tax exemption, Catholic officials said Wednesday.

The New York case involves the efforts of the Abortion Rights Mobilization to force the government to revoke the church's federal tax exemption on the ground it engages in impermissible political activity: its opposition to abortion.

The Reagan administration is fighting that effort in federal court in New York, and the National Conference of Catholic Bishops is no longer a formal party in that case.

However, U.S. District Judge Robert L. Carter ruled in May 1986 that the church had to turn over massive records about its political activities and its relationship with the Internal Revenue Service.

Carter cited the bishops with contempt of court and threatened them with $100,000 a day in fines but has put off enforcing the penalty while the church appeals.

A panel of the 2nd U.S. Circuit Court of Appeals in New York upheld his contempt citation in June by a 2-to-1 vote, rejecting the bishops' argument that Carter had no authority to hear the case.

It is the appeals court ruling that the bishops and associated church organizations appealed to the Supreme Court in a petition filed Sept. 11, officials said Wednesday.

In the new appeal, the bishops argued that Abortion Rights Mobilization was wrongly ruled to have legal standing to challenge the church's tax exemption while the church was ruled to have no standing to challenge subpoenas for records.

The appeal said such a decision "also creates an opening for the disruption of the orderly administration of the tax laws and the harassment of religious and other exempt organizations by politically motivated opponents using the process of the federal courts."