The White House released copies of President Carter's 1977 income tax return and a net worth statement yesterday that showed the president's overall wealth declined slightly last year and that he suffered a substantial loss from a trust set up for him when he took offce.

The trust, into which Carter placed his valuable holdings in farmland and the family's peanut warehouse business in Georgia, reported a loss of $306,271 last year that the president was able to deduct from his taxable income, according to the return.

But the return also showed that the trust, which is administered by Carter's longtime friend, Atlanta lawyer Charles H. Kirbo, paid the president $114,282 in dividends last year.

White House officials, arguing that the trust is "blind" and that neither they nor Carter is informed of its operations, said they could not explain the loss.

However, White House Counsel Robert Lipshutz said it is probable that the loss involved transactions of the Carter family peanut warehouse business, which represents a major share of the trust.

Coupled with other deductions and adjustments, the $306,271 loss allowed the president to reduce a gross income that totaled almost $500,000 to a taxable income of $121,826. He owed $48,152 in federal income taxes last year and is due a $35,161 refund from the government because of excess tax withholdings and an estimated tax payment he made.

The net worth statement listed the value of Carter's assets as of last Dec. 31 at $970,857, compared with assets valued at $1,048,039 at the end of 1976. The bulk of the president's assets at the end of 1977 consisted of the trust, valued at $557,717, and $204,979 in cash.

The president listed his liabilities at the end of last year at $175,500, almost all of it in anticipation of future income taxes on the appreciated value of his holdings. However, it is not known whether Carter actually will have to pay that much in income taxes if and when he sells his holdings.

Carter listed his net worth at the end of 1977 at $795,357, down slightly from a reported net worth of $822,638 at the end of 1976.

It appeared from a comparison of the net worth statements that the $306,271 loss the trust suffered may have involved the sale of one of the president's holdings. For example, the 1976 statement listed the "cost value," or purchase price, of three holdings that went into the trust at $359,436. In the 1977 statement, the cost value of the trust's toal holdings was listed at $151,097, suggesting some holdings had been sold.

While the White House continued to insist it did not know the details of the loss, it issued a statement last night attempting to clarify on apparent conflict in the loss trust suffered and $114,282 in dividends Carter reported receiving from the trust last year.

The statement quoted Kirbo as saying the dividend resulted from steps he took to fullfill Carter's pledge to divest himself of stock holdings in American Can Co.

The American Can Co. stock was owned by Carter's Farms, Inc., in which the president is a stockholder. To divest Carter of any interest in American Can, Kirbo said he transferred the can company stock to each stockholder in Carter's Farms, Inc. The $114,282 represented the value of the American Can Co. stock transferred to president. The can company stock was later sold, presumably for about its value at the time of the transfer.

Last year, Carter owed no income tax because of a business investment credit and voluntarily paid $6,000 in income taxes. White House press secretary Jody Powell said the president, because he is in the 50 percent tax bracket, will make another voluntary $6,000 payment this year in addition to his 1977 tax obligations.

In addition to his $200,000-a-year salary and a $50,000 expense allowance that is taxable, Carter listed as income $137,404 in royalties from the sale of his autobiography, "Why Not the Best?"

The president report $70,533 in deductions, including $38,520 in charitable contributions - $25,000 of which was book royalties turned over to a foundation that is planning a Carter presidential library - and $22,830 in state and local income taxes. He apparently spent only $1,371 of his $50,000 expense account - $413 for meals, $940 for gifts and $10 for flowers.

Under the law, Carter can convert the expense account to cash so long as he reports it as income, which he did.