"The person was caught and ended up going to prison for two and a half years."
He said one of the deer that was taken this time was "quite a good stag".
Mr Amos thanked police for trying to solve the crime.
"They have the arrow and are investigating where it may have been bought."
He said the club was going to install security cameras around Queen Elizabeth Park as a deterrent to future poachers who "may think twice" before killing another deer. It is not known if the thief will try to sell the venison on the black market.
Surfing the internet reveals deer meat sells for just over $6 a kilo.
An adult fallow deer buck is typically 140-160cm in length with a 85-95cm shoulder height, and weighs 60-100kg.
King and Henry Masterton hunting supply store owner Tony Roseingrave said either a crossbow or a longbow would be "very effective" against a fallow deer at close range such as the distance between the fence and the deer in Queen Elizabeth Park, especially if a "broad head" arrow was used.
A hunter at the store, who didn't want to be named, said he was "disgusted" at the idea of shooting nearly tame animals.
He said he regularly took his grandson to the park to hand-feed the deer.
Asked how difficult it would be to use a bow at nighttime, he said it would not have been difficult with animals like these.
"To be honest, he probably held out some food and they came up," he said.
"There's hunting ... and there's this."
Masterton district councillor David Holmes, who farms on Lees Pakaraka Rd, discovered a fallow deer carcass on the road outside his property last Thursday. It had been butchered, with just the carcass and hide remaining.
"Someone had definitely killed the animal and taken what they wanted."
He said six weeks ago he discovered the carcass of a cattle beast on his road, processed in the same manner.