Unaware the Tararua District Council has a 24/7 animal control service, the Jacksons rang the Dannevirke police, who arrived mid-afternoon on Saturday.
"We've now contacted animal control who are looking into the attack," Mrs Jackson said.
District council animal control staff have told the Dannevirke News on-call officers over the weekend responded to the call-out and staff were investigating.
Now the Jacksons are looking for a new home for their beloved goats.
"Andreas and Anton are so upset, so we've all decided we'd like someone on a farm to take both Chocco and Queenie," Mrs Jackson said. "But they've got to stay together because they're so close."
The goats are between 6 and 7 years old and the Jackson family say they're "beautiful and so friendly."