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The incident happened on Thursday night in the parking lot of Prestonwood Baptist Church in Plano, Texas, said the city's police spokesman, who downplayed reports that the singer was drunk at the time.
"Witnesses are reporting and our investigation revealed that Mr. Travis assaulted the husband," said Officer David Tilley, adding that Travis was a friend of the woman.
The exact nature of the contact remains unclear, but Tilley said neither the husband nor anyone else at the scene reported an injury. Travis' misdemeanor citation for simple assault is the equivalent of a traffic ticket.
"It must have been something very minor, I can tell you that," Tilley said, adding that a citation for assault can cover an offense such as unwanted physical contact.
The North Carolina-born country singer, known for hits like "Out of My Bones" and "Forever and Ever, Amen", will have to contact a local court to deal with the citation. Jail time is not normally administered in such cases.
Representatives for Travis could not be reached for comment.
Tilley disputed media reports Travis was intoxicated at the time of the dispute. "I've seen the reports and I don't know where they're getting this information," he said.
Earlier this month, Travis was charged with drunk driving and retaliation after a Texas state trooper found him lying naked on a road near where his vehicle had run into highway construction barriers, the Grayson County Sheriff's Office said at the time.