Travis was arrested early the morning of February 6 on a charge of public intoxication.
Travis apologized for his actions later that day.
In the dashcam video, officers can be seen approaching a black, late '90s Pontiac sports car parked in a church parking lot.
Officer Carl Parker knocked on the window and asked what was going on.
"Oh, I was asleep," Travis told him.
"Asleep? Do you have any ID on you," Parker said.
Travis couldn't find his ID but told the officer his name.
He said he was originally from North Carolina but was living in Tioga.
Travis' words were slow and slurred, prompting Parker to ask Travis if he had had anything to drink.
"Yes, sir, I have. But I am not driving, as you can see," Travis said.
At one point, Travis even asked Parker for a ride home.
"If you could give me a ride to the house I called in Tioga, I would be grateful," Travis said.
The video shows a few more officers arriving on the scene.
In the video, Parker went back to his car to talk to dispatch and calmly told the dispatcher what Travis just told him.
"Subject stating he is the Randy Travis and that he has a driver's license out of New Mexico," Parker, who is off camera, can be heard saying.
The dispatcher, seemingly stunned after recognizing the name, answered: "I don't know what to say."
"Do you want to send us a picture for verification?" the dispatcher said.
At that point, the officers asked Travis to get out of his car. Travis can be heard struggling to open the door before opening it.
"Here's what's going to happen tonight," Parker told Travis. "You're going to go to jail for public intoxication."
"Really? Are you kidding me?" Travis said.
Parker told Travis he needed more information about him.
"Maybe once we get to the jail, we can figure out who ... get some more information on you, who you are," he said.
"Are you kidding me?" Travis said.
One officer had earlier removed what looked like a wine bottle out of Travis' car.
When officers tried to get Travis in position to handcuff him, he said: "You fixing to put handcuffs on me, are you? Is that what you're fixing to do?"
"Yes, sir, I need your left hand, please," an officer said.
After walking Travis back to the car and putting him in the back, Parker stepped away from the car, with the dashboard camera still rolling and the mic still on, to discuss the situation.
The officers agreed that the man looked like Randy Travis, the famous country music artist.
They even pointed out that the name was on an insurance card.
One officer is heard saying, "Do what you got to do."
Another officer mentioned that Travis told him that he had been in an argument with his future wife.
The first part of the ride back to the Denton County jail was mostly quiet.
Over the radio, an officer said he found Travis' New Mexico driver's license.
But as they got closer to the jail, things got tense.
Travis asked Parker how many hours he had to spend in jail before he would be driven back to his vehicle.
Parker said it was usually four hours but told him he couldn't drive Travis back to his vehicle.
"Will anyone here drive me back to my vehicle?" Travis said.
"Now that, I do not know," Parker said.
"You don't?" Travis said. "You should. Don't you think you should know that? I think you should. Because I own the [expletive] vehicle, and I actually have a license, and I'm actually a state taxpayer. Yeah, yeah, you should know that, by the way."
While waiting for the gate to the jail to open up, Travis can be heard complaining about being in handcuffs.
"Yeah, put these [expletive] handcuffs on somebody who -- yeah, I'm about as threatening as a cat," Travis can be heard saying in the back of the car.
The gate to the jail opened and, before the camera shut off, Travis can be heard sternly asking for Parker's name.
"Officer Parker -- OK, thank you," Travis can be heard saying.
Travis' publicist said Tuesday that she and Travis had not seen the dashcam video.
His publicist said the country star might have a comment after they see the footage.