A relative of the 26-year-old woman, calling on her behalf from Reno, Nev., had asked for help from the sheriff's office just after 5 p.m. Sunday.
However, search-and-rescue missions generally avoid animal rescues, since such efforts could compromise response to developing emergencies involving humans, Cannon said.
The purported attack was unusual, he added.
"I've never heard of a mountain goal attacking anyone before up there," Cannon said. "Usually, they just run away."
Whatever led to the incident, Cannon said, the dog was no match for the horned goat, which can weigh in at 150 pounds.
The incident was not reported to the Utah Division of Wildlife Resources, but hearing about it was a first for Scott Root, manager of the agency's Central Region, which includes Mount Timpanogos.
"I can see it happening, though, if they got too close to the mountain goat. It could have seen the dog as a predator," he said. "In general, we tell people to keep a distance from any wildlife they may encounter."
DWR more often responds to reports of nuisance bears, wandering deer and elk and the occasional mountain lion coming out of the mountains. In such cases, the animals generally are trapped or tranquilized for relocation, and in rare cases considered dangerous, shot or euthanized.
But mountain goats?
"I've never heard of such a situation with a mountain goat before. I guess that would be up to a wildlife biologist to figure out," Root said.
In any case, no pursuit of the alleged hooved offender was planned.