The polls may be in a nose dive and public criticism at a peak, but in one important area - campaign fund-raising - President Carter seems to be doing just fine.

Financial records made public yesterday show that Carter has received just over $1.5 million in contributions to his reelection campaign in the three months since he started raising funds.

His original Georgia base - lawyers, farmers, bankers and friends from his home state - combined with corporate executives and corporate political action committees gives Carter a respectable showing in the latest filings with the Federal Election Commission.

Carter's campaign has received contributions of $1,000 - the most an individual can legally give - from such businessmen as Occidental Petroleum chairman Armand Hammer, Giant Food chairman Israel Cohen, and Dwayne Andreas, chairman of the Archer-Daniels-Midland grain firm.

The president also has taken in more than $65,000 in gifts from 50 different political action committees, including those run by Grumman Aircraft, Coca-cola, Chrysler, and Pan American, National, Delta, and Texas International air lines.

In total receipts, though, Carter is behind two Republican, presidential hopefuls who have been raising money for a longer time, according to quarterly finance reports filed this week.

The most prosperous of all the current presidential efforts is that of Texan John B. Connally, who reported total contributions of $2.2 million to his six-month-old campaign for the Republican nomination.

The biggest recipient is the most conservative candidate, Rep. Philip Crane (R-Ill.), who has taken in nearly $2.5 million since he announced his candidacy for the GOP nomination 11 months ago. But Crane has spent more than he has raised, and faces a $795,000 debt while contributions have slowed considerably.

Among the other Republicans, George Bush reported contributions of just under $1.5 million; Sen. Howard H. Baker Jr. (Tenn.), who has not formally announced, reported receipts of $643,373; Sen. Bob Dole (Kan.) reported $253,286, and Rep. John B. Anderson (Ill.) listed $201,000.

Ronald Reagan, the front-runner in most GOP preference polls, failed to file a financial report on time. Reagan, who has a national campaign committee but has not declared his candidacy, also failed to file a timely report for the first quarter of this year. Quarterly reports are required from candidates, announced or not, who are raising or spending money in pursuit of the presidency.

Most of the candidates' fund-raising efforts had clear regional concentrations. Carter's most fruitful areas were his native Georgia and Vice President Mondale's home state, Minnesota. About 75 percent of Dole's funds came from Kansas, and Baker's contribution center was Tennessee.

The two Texas Republicans, Connally and Bush, drew heavily from Texas sources, but they both seemed to be drawing funds from a broader geographic base than their opponents.

The broadest distribution of contributors shows up in Crane's reports. Crane, too, is the only candidate who reports the bulk of his contributions coming in small amounts. Unlike all the others, Crane got more than half his money in contributions of less than $100.

But Crane's reports show he is not attracting many new financial supporters. About two-thirds of the contributions he listed for the last quarter came from people who have given money to his campaign at least once before.

Connally's contributor list reads like a roster of the executive suites at Fortune's 500. His donors include the chief executives of Mobil Oil, Superior Oil, Phillips Petroleum, Marriott Hotels, B.F. Goodrich, Milliken textiles, and Olin Corp. Connally also seems to have an early lock on the grocery business; he received contributions from the presidents of Safeway, Winn-Dixie, Southland (7-Eleven), and Piggly Wiggly.

Connally received a $1,000 contribution from James S. McDonnell II of McDonnell Douglas Aircraft, but another member of the McDonnell family, Sanford, sent his support - $1,000 worth - to Bush.Bush also received money from PepsiCo chairman Donald Kendall, S.D. Bechtel of the Bechtel Group of industrial companies, and Herbert Kohler of te Kohler plumbing fixtures firm.

The new reports showed that many contributors are hedging their bets. Henry Ford II of Ford Motor Co. contributed to Carter and Bush. Insurance magnate W. Clement Stone gave to Connally and Bush, as did David Packard, an industrialist who left presidential appointments in the last two GOP administrations. Champion spark plug chairman R.A. Stranahan gave to Crane and Connally. CAPTION: Picture 1, PRESIDENT CARTER; Picture 2, JOHN B. CONNALLY