Police photographers and forensic analysts were called to the street about 10.45pm. The CIB was in charge of the investigation overnight.
Police said a 59-year-old man, who lived in a nearby unit, was found at the complex and offered no resistance when he was arrested.
He was charged with assault and will appear in Christchurch District Court tomorrow.
Detective Senior Sergeant Brian Archer said more serious charges would probably be laid. Canterbury Police were not seeking any other people in relation to the death.
Archer said the victim's identity was not yet confirmed but she was certainly a resident of the complex. The cordon was still in place overnight and police said they would carry out a scene examination today. Police investigators also hoped to talk to more local residents today.