Travis, 53, threatened to "shoot and kill" troopers investigating the case while he was being transported to jail, Grayson County Sheriff's Sergeant Rickey Wheeler said.
The singer, known for such hits as "He Walked on Water," was arrested late on Tuesday near his hometown of Tioga, about 60 miles north of Dallas.
The sheriff's department had received an emergency call of a man lying in a roadway, possibly because of a crash. A trooper found Travis, whose vehicle had run into highway construction barriers, Wheeler said.
"He was not clothed at the time," Wheeler said.
The singer refused blood or breath tests at the scene. He was taken to a hospital where a blood sample was drawn after a warrant was obtained, he said.
Travis was released on Wednesday on $21,500 bond on charges of driving while intoxicated and retaliation due to the threats against the troopers.
Retaliation is a third-degree felony. The drunk driving charge is a misdemeanor.
Travis was also arrested near Tioga in February and was charged with public intoxication.
Travis, a six-time Grammy Award winner, also has appeared in movies and television shows. He had a recurring role in the television show "Touched by an Angel."
A representative for Travis could not be reached immediately for comment.
(Editing by David Bailey, Ian Simpson and Vicki Allen)
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