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The organisation's executive officer Sophie McSkimming said although it was following positive leads, the SPCA needed more information.
There was a public outcry last month when the organisation said a 12-week purebred huntaway male puppy drowned after apparently being tied to a rock and thrown off the Alexandra Bridge.
''The community has been amazing but we just need more information to go on, before we can take action,'' Ms McSkimming said.
''We have some pieces of the jigsaw but can't complete the puzzle until we get the missing pieces of information from the public.''
She could not give any details about the information gleaned so far or the results of the postmortem on the pup as the investigation was still under way and that information could form part of the evidence in any court case connected with the incident.
The response to the Otago Daily Times story about the incident, posted on the organisation's Facebook page, was ''amazing'' and everyone seemed to be horrified about what happened, she said.
The black and tan puppy was found in the Clutha River on July 21 by a young fisherman. Its lead was tied around a schist rock.
Anyone with information about the incident can contact the SPCA on 0800 682-467.