Census officials have turned to the National Conference of Catholic Bishops to try to persuade several million undocumented aliens, predominantly Spanish-speaking Catholics, to be counted in the 1980 census without risk of deportation.

The Catholic bishops, however, have held off from making a move until President Carter gives some kind of public guarantee that census data would be kept confidential, a guarantee already provided by law.

Both Vincent P. Barabba, the new director of the Census Bureau, and Rep. Robert Garcia (D-N.Y.), who heads the House subcommittee on census and population, made the request for help to Archbishop Robert F. Sanchez of Santa Fe, chairman of the U.S. Bishops' Committee on Hispanic Affairs.

"We're caught in the middle," said Paul Sedillo, director of the bishops' secretariat for the Spanish-speaking. "The Hispanic community wants a good census, both because of federal financial grants to cities based on population and because of congressional representation, which is apportioned according to population.

"But the church is not going to risk its credibility with Hispanics who don't trust any institution except the church without some sort of public presidential assurance," said Sedillo.

The Rev. Francisco Dominguez, head of immigration services for the archdiocese of New York, confirmed that census officials have approached his office for help. "We're very leery of this whole thing," Dominguez said. "After all, we almost don't trust the government ourselves. We have been getting the runaround for years in our attempts to get new immigration legislation and amnesty for people already here without papers."

But Dominguez conceded that registering undocumented aliens in the census would help bring much-needed federal aid to depressed inner city areas in which many Hispanics live. The priest said that 60 percent of the estimated 700,000 to 1 million undocumented aliens in the New York City area were of Hispanic origin.

A New York City official told the House Select Committee on Population last year that the inclusion of 750,000 undocumented aliens in the federal revenue-sharing formula would result in an additional $20 million a year to New York City and an additional $3 million in community development funds.

According to Vilma Martinez, president and general counsel of the Mexican American Legal Defense Fund, Cardinal Timothy Manning of Los Angeles has agreed to hold a "Census Sunday" in his archdiocese, where Hispanics form about 30 percent of the population. Priests in the archdiocese's 178 parishes will urge people to register in the census.

Sedillo attributed the church's credibility to the human rights stance it took in Latin American countries and to the church-sponsored grass-roots organizations aliens find in most American cities.

Sedillo pointed out the added advantage of having nine Hispanic bishops in the Catholic hierarchy -- all appointed since 1976. Six are auxiliary bishops. Three are the heads of dioceses.