Police are also seeking information on two vehicles of interest that were spotted on CCTV footage in the area around the time of Tolley's death. They are a blue Subaru and a silver, lowered, sedan-type car with black wheels.
Barnett said police were trying to either eliminate the vehicles as unrelated, or include them into the investigation.
The suspects:
Suspect one is a tall male, around 1.88m with a skinny build, aged 20s to 30s. He was wearing dark, baggy clothing, a hoody with the hood up, dark, low-slung pants, and possibly white underwear. Police also say he was carrying a large, rectangular object.
Suspect two is a male, shorter than the first suspect, with a skinny build, who was wearing dark, baggy clothing.
Suspect three is a tall male with a lean build, wearing dark clothing, long dark pants, and a hoody with the hood up.
Suspect four is a male that "sounded younger than the other suspects" and is believed to be the man who was seen upset outside Tolley's flat, Barnett said.
Anyone who has not yet spoken to police but who may have information that can help should contact the Operation Archer team based at Upper Hutt Police Station.