Vice President Bush today released income tax returns showing that he and his wife paid about 37 percent of their income in federal taxes over the last three years, but $144,000, plus interest, was paid under protest last June because of an under- payment in 1981.

Bush released his tax forms after amending the blind trust he had set up when elected vice president. Earlier, he had said the terms of the trust prevented him from seeing or disclosing his tax returns.

The returns released today show he and his wife, Barbara, paid $303,421 in taxes on an adjusted gross income for 1981-83 of $810,477.

On an annual basis, the percentage of income paid to the federal government declined over the three years. In 1981, Bush paid about 49 percent in taxes, including the protested back payment. In 1982, he paid 24 percent and last year 13 percent. If he wins his IRS dispute, his tax rate over the period will drop to 28 percent.

Over the three years, Bush listed more than $24,275 -- or about 3 percent of his income -- in charitable contributions.

Bush paid the added $144,128 -- plus about $54,000 in interest -- on his 1981 taxes last June, according to his lawyers, after the IRS ruled against him on two 1981 transactions.

In the first case, the Internal Revenue Service ruled Bush was not eligible to claim a house he purchased from an aunt in Kennebunkport, Maine, in 1981 as his prinicpal residence, although it is the only house he owns. As a result, he was unable to "roll over" and not pay taxes on a $496,000 capital gain from the sale of a house in Houston.

Bush currently resides in the vice president's official residence, Admiral's House at the Naval Observatory. His lawyers, in a statement released today, said they argued that the Kennebunkport house is "where they Bush and his wife have their furniture, their books and their personal belongings -- it is the Bush family center."

Bush maintains a voting address in Houston. He owns a lot there and intends to build a house and live there in the future, according to Shirley Green, his deputy press secretary.

The Kennebunkport house is valued at $950,000 and represents almost half of the Bushs' net worth of $2.1 million, according to a statement released earlier.

The second dispute involved the disposition of funds left over from Bush's 1980 presidential campaign. The IRS ruled that Bush improperly excluded from his income all but $5,000 of $32,807 he had given to the Republican National Committee. The money was left over from his unsuccessful 1980 presidential campaign.

The IRS also ruled that another leftover amount, $26,362 used by Bush to redecorate his vice-presidential office, had to be included in his income but could be claimed as a deduction. It said $2,449 he used to pay late campaign expenses had to be declared but could not be deducted.

Dean Burch, Bush's lawyer, said he felt the funds had been transferred to a qualified political organization and should have been eligible for the exclusion.

Burch said Bush has directed his lawyers to appeal the IRS decisons and prepare to file suit against the IRS if necessary. Bush knew about the tax problems because the Kennebunkport house has never been part of the blind trust that contains his stocks and securities.

Geraldine A. Ferraro, the Democratic vice-presidential nominee, released her tax forms and those of her husband, John Zaccaro, in August during a controversy about their finances. The forms showed that they paid about 40 percent of their gross income in federal, state and local taxes.

Bush said today he hoped the release of his tax returns would satisfy the "insatiable curiosity" about them. He said he believed he had dealt properly with his financial holdings by establishing a blind trust in 1981. Under the terms of the blind trust, Bush does not review or sign his tax returns.

Before becoming vice president, he released eight years of tax returns.

He called today's release "total disclosure, total and full . . . the whole schmear." He said that, in the future, he plans to retain a blind trust but make out his own taxes. "I'll do anything to get out from under this flak.

"What I might do when this election is all over is change the trust to still protect the public interest but not go quite so far as I went," he said. "There is a way you can do it where you sign your tax returns and still do not know your holdings. President Reagan has such a trust. I think in retrospect I wish I'd done that."

Asked if he sympathized with Ferraro over the issue, he smiled and said, "Yes."

Bush's lawyers also released today a letter from David H. Martin, head of the Office of Government Ethics. Martin said his office had not pressured Bush to amend the trust and "would have preferred not to disturb it."

But it was a statement from Martin last week, in which he said Bush was not barred from releasing tax information, that set off the chain of events that resulted in today's disclosure.

The information released today showed that in 1981 Bush had adjusted gross income of $504,829 and paid $245,491 in taxes. As originally filed, he showed adjusted gross income of $260,107 and paid $101,376 -- about 39 percent -- in taxes. In 1982, Bush had adjusted gross income of $163,531 and paid $39,625 in taxes. Last year, his adjusted gross income was $142,117 and taxes were $18,305.

Bush paid no state or local income taxes in 1981 because neither Texas or the city of Houston has an income tax. In 1982, he paid $988 to Maine in non-resident taxes.

Bush's income as vice president was $91,000 in 1983, according to Robert B. Yorty, one of Bush's lawyers.

Bush sold his Houston home in 1981 for $843,273, later purchased the Kennebunkport house from his aunt for $780,800, according to the tax returns, and used another $90,000 to remodel the house.

The IRS ruled that the Kennebunkport house was not the Bushes' "principal residence" because they had not lived in it either in the two years before or the two years after the sale of their Houston home.