The State Department yesterday proposed that the 52 former hostages be declared eligible for free medical and psychiatric care as well as liberal education benefits when they return home.

Under a law passed last fall, they already are exempt from federal taxes on money earned while they were imprisoned.

But whether they will receive any additional compensation remains undetermined. Jimmy Carter, in his final hours as president, signed an executive order prohibiting the former hostages from suing Iran for damages resulting from their captivity.

The 52 Americans, however, will have recourse to a commission to be set up to handle their claims. Carter's order said that the yet-to-be-named commission would consider whether compensation, if there is any, should be made by Congress, or awarded by the president to the ex-hostages and their families.

Under regulations to be published in today's Federal Register, the State Department proposed that any hostage, or hostage family member, be declared eligible for free medical or psychiatric care for any illness caused or aggravated by the hostage situation.

Hostages wanting to change jobs or get additional training because of their experiences in captivity would also qualify for a living allowance and free tuition, books and supplies. Their children and spouses would be eligible for the same assistance.

Several hostage families are negotiating with various news organizations and book publishing firms over rights to their stories, and are expected to receive sizable amounts of money. A number of airlines have offered free airfare to the former hostages and their families.

Each of the 52 can also look forward to receiving $207 from a fund-raising drive organized last fall by a Glenview, Ill., public relations man. Merton G. Silbar had hoped to raise $1 million for the hostages, but his U.S. Hostage Fund was able to collect only $11,000.

"We know we tried to do something," Silbar said. "We did a little more than shake our heads."