The Smoaks told CNN that as they knelt, handcuffed, they pleaded with officers to close the doors of their car so their two dogs would not escape, but the officers did not heed them.
Pamela Smoak is seen on the tape looking up at an officer, telling him slowly, "That dog is not mean. He won't hurt you."
Her husband says, "I got a dog in the car. I don't want him to jump out."
The tape then shows the Smoaks' medium-size brown dog romping on the shoulder of the Interstate, its tail wagging. As the family yells, the dog, named Patton, first heads away from the road, then quickly circles back toward the family.
An officer in a blue uniform aims his shotgun at the dog and fires at its head, killing it immediately.
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Cookeville Police Chief Robert Terry released a statement on the department's Web site Wednesday night describing the department's regret over the incident. The Cookeville Police Department site was not responding Thursday morning.
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"No one wants to experience this kind of thing, and it's very unfortunate that it occurred," he wrote. "If we had the benefit of hindsight, I'm sure some -- if not all of this -- could have been avoided. I believe the Tennessee Highway Patrol feels the same way."