Auckland police are seeking information about a white station wagon, in relation to the murder of Lena Zhang Harrap.
The 27-year-old was found dead near a walkway in Mt Albert on Wednesday.
Harrap, who had Down syndrome, failed to return home after going out for a walk.
A 31-year-old man has been remanded in custody after being charged with her murder and sexual violation. He has been granted interim name suppression until his next appearance in the High Court at Auckland on 13 October.
Detective Inspector Aaron Pascoe said information from the public is helping the investigation team to piece together what happened.
Police are still seeking any sightings of the vehicle, a white 2004 Hyundai station wagon with the registration EGZ962, which was used by the alleged offender.
It has distinctive brown tape around the left rear window.
Police are not seeking anyone else in relation to the death, but said anyone with information relating to the case, or who had seen the vehicle in question, should call 105 and quote the file number 210922/0539.
Pascoe said police expect to complete their scene examination today.