The Iowa Policemen's Association convention is hardly a place to find sympathy for a millionaire who paid no state income tax, especially if she's a woman who wants to become governor.

It is a no-nonsense affair, attended by big beefy cops, underpaid and overworked. They are hardly pushovers.

Yet listen to what some had to say about the tax problems of Roxanne Conlin, a liberal Democrat seeking to become the state's first female governor.

"That doesn't bother me one bit," said Bob Klein, a district court bailiff in Du-buque, a river city reeling from hard times. "That's the game. The more money you make, the less you pay in taxes."

"I'm a Roxanne backer," said Chuck Werrington, a veteran policeman from Davenport. "When I first heard about the income tax thing, I was quite upset. But hell, she didn't do a damn thing you or I wouldn't have done. If I had a tax shelter, I'd use it."

Eight others offered similar comments, part of a powerful political message echoed in recent polls: Iowa again has a real governor's race.

Conlin, 37, a former U.S. attorney, was left reeling last summer after she revealed that she and her husand, James, a real estate developer, paid no state income taxes in 1981, despite a net worth of $2.2 million.

But in recent weeks, Conlin, who had lambasted Republicans for belonging to "the party of privilege," has made the year's political comeback. According to the latest Iowa poll, she has moved within four percentage points of Lt. Gov. Terry Branstad.

"The one issue all summer long was my personal tax situation," Conlin said in an interview. "It really hurt me among poor people, the elderly and blue-collar workers. People were thinking, 'This woman is worth $2.2 million. How can she relate to the problems of survival?' But now people have become impatient with the issue. They've decided it isn't material to the future of the state."

Branstad, running with the support of popular Gov. Robert D. Ray, who chose to retire after 14 years in office, attributes Conlin's gains to "a natural coming-home effect" among Democrats.

The focus of the race has shifted to jobs and the economy. Conlin has proposed borrowing $300 million for a public works program "to put Iowans to work," while Branstad has offered tax incentives to attract industry.

At one recent debate, Branstad, 35, charged that Conlin's plan is "a cruel hoax" that would take two or three years to have any impact.

Conlin shot back: "The cruel hoax is to pretend that trickle-down economics is working, or will work, or will benefit the people of this state in any way."