"We're still piecing together what has actually happened," she said.
"We need to speak to the other two people who were involved to work out what has actually happened. At this stage we don't know that there was cannabis involved."
Ms Dunn said police could not yet say whether any charges would be laid.
However, they had been speaking with the SPCA to see whether there was "potential ill-treatment of an animal".
Ms Dunn agreed the photo was disturbing.
"We've had a pretty significant response from the community, coming to us and expressing their distaste for what these kids have done on Facebook, so there's been a lot of people very unhappy with their behaviour.
"Whether or not there's any actual criminal culpability, we don't know that yet."
Nelson SPCA inspector Craig Crowley said the incident was concerning.
"But in reality, a lot of the blame should be laid at the foot of their parents - 14-year-old kids doing this sort of thing is just a lack of parental control."
Mr Crowley said under the Animal Welfare Act, parents were responsible for the actions of children under the age of 16.
He said the maximum penalty for ill-treatment of an animal was a $10,000 fine or six months in prison.