Police and animal control officers lost sight of the goat as it ran through properties, jumping fences.
Later that day, police received a call from an Oamaru woman who reported a large goat had been bailed up in her garage by her dog.
Snr Const Pedersen confronted the goat, which had damaged the woman's property, including her mobility scooter.
He admitted his decision to use his Taser might have been considered "a bit drastic" but given the circumstances he felt it was the best decision for all concerned.
He said animal control made the decision to put the animal down, but not because of injuries caused by the Taser.
Waitaki District Council policy and communication manager Mike Roesler said the situation was dangerous and the decision was made to put the animal down.
"My understanding is the animal had no life-threatening injuries at the time it was put down.
"The decision was made purely from a public safety perspective.
"The animal was agitated, distressed and posing an immediate public safety risk prior to the tasering.
"This was a large agitated male goat."
People at the scene, including a local vet, were unable to calm the goat, and it would have continued to be a safety risk had it escaped again on to the nearby state highway, he said.
The owner of the goat is still unknown.