Richard A. Viguerie, the conservative direct-mail expert, has switched Republican presidential candidates and gone to work for John Connally.

Viguerie, one of the most controversial figures in what he calls "the New Right," had worked with the campaign of Rep. Philip M. Crane (R-iii.) for more than a year. But their relationship had been on shaky terms since last March, when Crane aides accused Viguerie of deceptive business practices.

The decision to part ways was apparently a mutual one.

"He [Connally] is not as conservative as I am, but he's conservative enough," Vigurie said."Besides, I'm a pragmatist. Of all the candidates out there I think Governor Connally has the best chance of being nominated. I think the conservative movement should support him. In four or eight years, we can try to work for someone more conservative."

Viguerie, whose various firms added more than $1.6 million to Crane's coffers, said he intends to work as a volunteer for Connally, overseeing his direlt-mail fund-raising efforts.

He said, however, that firms he controls may handle some of Connally's direct-mail activities.

Viguerie raised more than $2.5 milliom though direct-mail appeals for Crane, according to Federal Election Commission reports. But 64 cents of Every dollar collected went to companies affiliated with Viguerie to defray costs.

Winton Blount, Connally's campaign chairman, said the addition of Viguerie "is a tremendous plus. His track record in political fund raising, voter solicitation and volunteer identification is legend."

Crane's campaign, meanwhile, mimimized the impact of the loss. "We basically have gotton everything that Richard Viguerie can give us," said Crane press secretary Laura Brodrick. "We had intended to phase Richard Viguerie out all along in September."

Viguerie's clients in the past have include former Alabama governor George C. Wallace, Sen. Jesse Helms (R-n-c-."), for whom he raised $8 million in 1978, and a host of conservative members of Congress.

He controls mailing lists that contain names of 4 million political conservatives, and he holds joint ownership in a list of 83,000 names of people who have donated to Crane. Legally, he could use the Crane list to raise money for Connally, something he said he doesn't intend to do.