Detective Inspector Virginia Le Bas, who has worked on the case from its early stages when Hayden went missing on August 22, said police were restricted as to what they could say.
"An arrest has been made, so it's quite different from when we sometimes find a body or whatever and we can talk a lot more. But we're in a situation now where the arrests have already been made and it's all before the court."
Ms Le Bas said it was difficult to estimate how long police would remain at Ruru Lawn Cemetery.
Activity at the scene, where three large police tents have been erected in the eastern corner of the cemetery, has noticeably decreased since the human remains were recovered.
Private security guards continue to patrol the cemetery's perimeter. Mourners unconnected to the Miles case have been allowed into to the cemetery grounds but are told to keep their distance.
Hayden was robbed of a cask of wine hours before he was murdered, police allege.
A 27-year-old man appeared in court on Monday charged with his murder and two others have been charged in relation to Hayden's disappearance.
An 18-year-old woman, granted name suppression, is accused of being an accessory after the fact, while a 35-year-old man, is charged with robbing Hayden of a cask of wine on August 22 - the last day he was seen alive.