A scene examination at the Glenvil Lane home where the 69-year-old was found dead by her daughter and son-in-law on Friday night is also ongoing.
Detective Senior Sergeant Roger Small said a police specialist search team have carried out an extensive examination of the property and neighbouring area.
A team of around 25 investigators are working on the case including forensic experts.
Mr Small said a special phone number set up for the investigation had only received a few calls. He urged anyone with information to contact police.
"Though we are getting a pleasing level of assistance from Te Atatu residents, I can't stress enough how much we need to hear from anyone who has seen something or someone who appeared suspicious or out-of-place on Friday, or in the days before" he said.
"If you've noticed anyone hanging around or anyone behaving in a way you thought was odd, or a family member perhaps acting strangely, we want to hear about it, please call the 0800 number."
Mrs Tian's body was removed from the house yesterday and a post mortem examination is expected to be completed today.
Mr Small will not be drawn on Mrs Tian's cause of death, her injuries or any weapons police are looking for.
He is expected to release more information about the investigation, dubbed Operation Nepal at 3pm today.
A vigil will be held on Tuesday to remember Cunxiu Tian, whose body was found by relatives at her Te Atatu home on Friday.
Te Atatu Baptist Church leader David Spackman announced at a service this morning that the vigil will be held to remember the slain neigbour, Radio New Zealand reported.
"It's pretty sad news really to happen in our community," Mr Spackman said."We just need to get back to the community and back to what the community is about because I don't know what's going on but I'm sure we can stand against it... It's just not right what's happening at the moment."
The church is two doors away from the the house, where a police cordon was still in place.
Those attending the service this morning listened to a prayer for her grieving family member from congregation member Nicola Hubble, who said Ms Tian has been killed "so tragically, so close to our church".