John Connally is a handsome man, more serious-seeming than Ronald Reagan. Equally effective on the stump, if not quite so witty, the homilies he recites seem less contrived.

For example, Reagan delivers the familiar conservative attack on government by citing individual horror stories, often so outrageous or funny as to suggest the work of a ghost writer.

Connally makes the same points without resorting to anecdote. Partly as a result, he seems more heavyweight than Reagan, and if Republicans should regard Reagan at 68 as too old to be their candidate, Connally at 62 is certainly ready to serve.

Nevertheless, and despite those advantages, a Connally candidacy would be a major mistake for the Republican Party, as well as for the country.

First, for the embarrassment to the party. Connally was indicated for taking a bribe in the famous milk scandal of the Nixon years. I hasten to add that he was found not guilty after an able defense by one of the country's great trial lawyers.

But if his party nominated him for president, it could hardly ignore that important event in his life. Do Republicans want to spend their campaign money explaining the milk scandal and how their candidate was only on the fringe of it and was found not guilty and so it doesn't really matter and the voters should ignore it, etc, etc.?

It's true, of course. The voters should ignore it. But wouldn't the party be better off with a candidate who had not been indicted?

Then, too, Connally is known among his former colleagues in the Nixon administration as a bull in a china shop. Almost to a man they dislike him and recall him as having been overbearing and rude.

I don't discount the possibility of jealousy. Nixon regarded Connally the way small boys regarded professional quarterbacks.

But after what happened to Nixon, his former appointees are not longer jostling each other for his favor. They criticize Connally for being rude and overbearing to foreign officials engaged in trade negotiations.

"We were lucky to come through those times," one of them recalls, "without animosities turning into crises."

Being overbearing or throwing your weight around may not be a detriment in a political campaign because voters don't see it. But the fact that many of Connally's former associates, Republicans all, don't like him very much would not help him as his party's candidate.

Then there is Connally's change of parties. He was a life-long Democrat, an aide to Lyndon B. Johnson, secretary of the Navy to John F. Kennedy and a Democratic governor of Texas. Why the sudden switch? Connally explains it in terms of ideology. He cites the usual litany, linking Democrats with big government and bureaucracy. But if there's any truth to that charge, Connally ought fairly to be among those placed on trial. Many in his new party believe that he switched because Richard Nixon offered to back him for the Republican nomination in 1976.

Finally, Connally's ideology is very hard. When Ronald Reagan tells us that big government is interfering with the economy and that private enterprise should be freed to do the job, we somehow know that he isn't serious and that, behind the oratory, Reagan understands that the last thing the private-enterprise system wants is to be freed from government subsidies, government tax breaks, government tariff protection, government rate regulations and government bill collecting.

Not so with Connally. He might actually mean what he says. That would be a hard burden for the country to bear.