“There’s still a strong strain of the Kansas electorate that looks at that kind of behavior — even going to a strip club — as very inconsistent with their religious values,” said Chapman Rackaway, a political-science professor at Fort Hays State University in western Kansas.

Politico drew national attention to the report, which was published in The Coffeyville Journal, a small newspaper in southeast Kansas that publishes twice weekly. The paper has no website but the story spread over social media sites, including Twitter postings that showed the front page of The Coffeyville Journal with the headline, “Dem Governor candidate present at drug raid in 1998.” Mr. Davis, 42, a longtime state representative who is the House minority leader, declined an interview request Sunday, but in a brief statement said he was a lawyer for the owner of the Coffeyville, Kan., club and was in the building when officers arrived.

“When I was 26 years old, I was taken to a club by my boss — the club owner was one of our legal clients,” Mr. Davis said in the statement. “While we were in the building the police showed up. I was never accused of having done anything wrong, but rather I was in the wrong place at the wrong time.”

Mr. Brownback declined through a campaign spokesman to comment on the report, but the Kansas Republican Party’s executive director, Clayton L. Barker, said the incident provided insight into Mr. Davis’ character.

“Now the question becomes, as an individual, is he fit to govern?” said Mr. Barker, who added that the Democrat had revealed little about himself during the campaign and instead focused on Mr. Brownback’s policies.