John B. Connlly, the tough-talking former Texas governor, raised more than $2.085 million for his presidental campaign in the last three months, far outdistancing his rivals for the Republican nomination.

At the same time, contributions to President Carter's reelection committee were down more than 40 percent over the preceding three months, according to financial reports filed yesterday.

Connally has raised $4.3 million since January, and, almost 41/2 months before February's New Hampshire primary, he has more than $1 million in the bank.

Connally, who was secretary of the treasury in the Nixon administration, has mined a virtual who's who of the American business establishment to build his warchest.

He has done this at a time when at least three Republican rivals -- former California governor Ronald Reagan, Sen. Bob Dole (Kan.) and Rep. Philip M. Crane (III.) -- are suffering financial problems, and donations to Carter's reelection effort have dropped dramatically.

The Carter-Mondale Reelection Committee raised $854,000, or less than $10,000 a day, from July 1 to Sept. 30, a period of political unrest among Democrats. It raised $1.5 million, or about $16,000 a day in the previous three months.

With $886,764 on hand, the Carter-Mondale committe is not in financial trouble, and campaign officials insist their fund-raising activities are on schedule.

Evan Dobelle, Carter's national campaign chairman, said the committee had decided not to try to raise money in August, traditionally a poor month for political fund-raising.

"We're exactly on target," Dobelle said. "We're proceeding on schedule. We're not at all concerned."

But the fact remains that Connally, Reagan and George Bush, a former U.N. ambassador and CIA director, outraised the president.

In addition, a Florida committee formed to draft Sen. Edward M. Kennedy (D-Mass.) for president has raised $190,000, most of it in the last month.

The reports, required by law to be filed with the Federal Election commission, giva a number of other birdseye glimpses of the 1980 presidential campaign. Among them:

Reagan, the acknowledged front-runner for the GOP nomination, has a lingering, but perhaps not severe, financial problem. Although he raised $1.3 million the last three months, his campaign is $300,000 to $500,000 in debt.

Crane, a longshot conservative candidate, has been unable to recover from the financial problems that began to plague him last spring when almost. His campaign is $793,000 in debt, about where it was july 1.

A squabble with his former campaign manager has left Dole $166,000 in debt. But much of it is in dispute and Dole refuses to pay it.

Among the other Republicans, the campaign of Bush appears to be on the most solid footing. Reports showed he raised just under under $1 million since July and has $147,384 on hand.

Bush has raised $2.4 million since the start of the year; Reagan $2.7 million, Connally $4.2 million, and Senate Minority Leader Howard H. Baker (R-Tenn.) $1.2 million, more than $500,000 since July. Crane is another fund-raising heavyweight, with $2.7 million since he began campaigning almost 14 months ago.

Of the $190,000 raised by the Florida for Kennedy committee, at least $40,000 came in donations over the normal $1,000 limit on political contributions, indicating Kennedy forces have benefited substantially from a recent FEC ruling exempting them from the ceiling. The ruling allows contributions up to $5,000.

Last week, the Carter reelection committee filed a complaint with the FEC to protest the decision. It got an unexpected boost yesterday from Fred Wertheimer, senior vice president of Common Cause. In a letter to the FEC, he urged a prompt reconsideration of the ruling, saying "the issues raised by this complaint are serious."