Rose Kwan, who goes to a Bible-group meeting on Sundays in neighbouring Gloria Ave, said news of the homicide had put people on edge.
"At our prayer meeting, we prayed for the soul of Madam Tian, but we also prayed for our own safety," she said. "Our prayer leader told us not to walk alone because the attacker was still out there."
Neighbour Paul McGrath, who lives two houses away from Ms Tian, said: "This is a funny neighbourhood. I used to live in another cul de sac where everybody knew everybody. But this one here, people keep more to themselves."
Mr McGrath said he did not know Ms Tian or her family, but news of the violent death came as a total shock.
"First thing we wondered was who would kill an old lady," he said.
"Then when we heard it was a burglary, well gee that's just horrible. Then you think who else are they trying to break into."
A vigil would be held by the Te Atatu Baptist Church on Tuesday to remember Ms Tian, worshippers at the church were told today.
People in the community were asked by police today to examine the exterior of their properties to check windows and doors.
"If you notice anything untoward, leave it as it is and contact the police," Mr Small said.
He also asked residents to recall their movements and what they did between 9am and 5.30pm on Friday.
"Think back to family members, flatmates, house guests that came back into their house and how they behaved that evening," Mr Small said.
"Whoever was responsible ... would have been acting unusual and I'm sure one of you would have some suspicions."
Mr Small would not be drawn on Ms Tian's cause of death, her injuries or whether police were looking for any weapons.
He said the investigation was in its early stages and police were keeping an open mind on what had happened.
"I appreciate this is a frightening ordeal for the Te Atatu community and I think it's important that people are always conscious of their personal safety," Mr Small said. "I ask everybody to be vigilant about that, and I assure you that police are doing everything we can to identify this offender and bring him to justice."
The Operation Nepal team has about 25 investigators and additional specialist staff, including criminal profilers.
Detectives were back at the scene in Te Atatu today canvassing the wider area and speaking to residents.
"One of our lines of inquiry is the possibility that the offender has attempted to break into other properties in Te Atatu before Friday," Mr Small said. "It may be that residents haven't noticed this and we need people to check for us."
