He said enquiries were initiated to try to establish the circumstances that led to injury.
Inspector Taylor said on Saturday a member of police staff informed Whakatane Police that he was the person responsible for firing the arrow.
"Since becoming aware of the involvement of a police member, a senior officer has spoken to the owner of the dog to update her and to provide assurance that the matter will be investigated thoroughly and with integrity."
Ms Wallace said at the time she was shocked by the incident.
"When it happened I was in a state of disbelief, all I kept thinking was 'we need to get him to a vet or he'll die'. It wasn't your average Wednesday night."
Ms Wallace said she was surprised when she had found out a police officer was the culprit.
"I just couldn't believe it had actually happened, it didn't have to go that far and it was lucky Zeta wasn't killed.
"But in saying that, people don't just go around shooting dogs with arrows for no reason so something must have happened to upset the officer."
Ms Wallace said the whole incident was unfortunate and she was relieved Zeta had survived.
"We were really lucky that he bounced right back and is doing well again. The outcome could have been a lot worse so now we want to make sure something like this never happens again."
Inspector Taylor confirmed a criminal investigation was under way and an employment investigation would also be conducted.
Under the Animal Welfare Amendment Act 2010 it is an offence to willfully or recklessly ill-treat an animal.
Ms Wallace said she had recovered from the initial shock and was now "over it".
"There is no point being bitter about the whole thing. Yes, he did handle the situation inappropriately, but we're all human and we all make mistakes.
"We don't want him to lose his job because everyone we've talked to has said he's a nice, family guy, we just want an apology."