The Roman Catholic Church is planning a nationwide telecommunications network, using satellite and cable, which eventually could link every parish, parochial school and Catholic hospital in the nation.

In addition to transmitting TV programming for a wide variety of audiences, the network, expected to be operational by the fall of next year, may eventually provide the church and its myriad institutions with their own private postal and telephone system nationwide.

Establishment of the satellite communications system "is comparable to the decision the church in this country made when it decided to build a school system," said Richard H. Hirsch, secretary of the U.S. Catholic Conference's communications department.

The church's decision to use the latest technology to spread the gospel was explained by Bishop Norbert F. Gaughn of Greensburg, Pa. "Would St. Paul be using the satellite today? You bet he would," said Gaughn, head of the hierarchy's communication committee, at a meeting of Catholic communication officials earlier this year.

Initially the New York-based network will transmit 25 hours of programming a week, but eventually it is expected to operate around the clock. To participate, local dioceses must install dish-type receivers to decode and bring the signals from the satellite to earth. Programs will be recorded locally and aired over cable or commercial facilities, depending on arrangements worked out by local church leaders. They can also be made available to parishes, schools or even individuals with home video recorders.

To date, Hirsch said, 71 dioceses -- the Washington archdiocese among them -- have signed up to be part of the network. He estimated dioceses' initial costs for the hardware necessary to participate -- the receiving dish and recording equipment -- at about $30,000. Local dioceses will pay an annual membership fee of $5,000, plus additional fees based on the type and amount of service used.

During the 1950s, the late Archbishop Fulton J. Sheen made history in the then-new television medium by luring substantial numbers of the viewers from comedian Milton Berle, but in recent years it has been the conservative Protestant evangelists who have garnered both the ratings and the contributions -- a phenomenon frequently lamented in Catholic hierarchy meetings.

Hirsch emphasized that the projected new telecommunications network was not to be viewed as the Catholics' answer to Rex Humbard and the 700 Club. While the network will distribute some material for general audiences, he said, it also will produce more specialized programming, such as religious educational material for use in parochial schools and local parishes. He also cited the "enormous potential in the in-service training of staff personnel" in the 640 Catholic hospitals around the country.

The new system also offers the possibility of using the satellite linkage to share expensive medical diagnostic equipment, such as the highly sophisticated CAT scanner, a new application of X-ray technology, Hirsch said.

Planners of the new communications network believe the system ultimately could provide both a cheaper and more efficient internal communication system for the church with its 170 dioceses, nearly 19,000 local parishes, schools, colleges and hospitals. According to church officials, the Catholic Church nationally has an annual telephone bill second only to the U.S. government's.

An electronic mail system is another possible use of the system, Hirsch said. "When the bishop wants to write a letter to the parish priests, he puts it into the system and within five minutes a piece of paper comes out with the letter on it," he explained.

"It's the aggregate of services that makes this kind of system useful," he said.

Funding for the telecommunication network is coming largely from a new annual communication collection that the bishops authorized in 1978. Hirsch said $4.5 million is budgeted for starting costs.

A nonprofit corporation for the network is expected to be established within a month, Hirsch said, independent of the hierarchy but with bishops making up about 60 percent of the board members. The church currently is advertising for a director of the system.

Hirsch said there have been conversations with other religious groups, such as the National Council of Churches, about sharing facilities in the future.