Ms Farrall's body was found in the boot of her car at a Woolston supermarket on Sunday.
Police say the car had been there since 10am on Saturday.
Senior Sergeant Darryl Sweeney said this afternoon that police were making "good progress'' in their homicide inquiries.
The 38-year old, arrested on West Coast at 3am on Monday, was originally taken to Grey Base Hospital but was driven by ambulance under police guard to Christchurch Hospital this morning.
He remains in hospital in a stable condition under police guard, and was due to undergo surgery today.
Investigators say they interviewed him this afternoon.
A post-mortem examination on Ms Farrall, a 24-year-old community support worker, is continuing, police say.
They confirmed that the 38-year-old had lived at Ms Farrall's address at Wildberry St, Woolston, for a short time.
Forensic examination at the property continued today and will continue for some days, according to police. Forensic examinations of the two motor vehicles of interest are also continuing.
Police family liaison and Victim Support are continuing to provide support to her family. A team of up to 30 police staff are working on the investigation.
No charges have been laid in relation to either the homicide or the attack on the two tourists, and no court appearance is scheduled.
Both of the female tourists - a 27-year-old of Japanese/Dutch heritage and a 28-year-old from Germany - remain in Christchurch Hospital in a stable condition.
Police spoke to the two women last night and hope to speak to them again tomorrow.
Police are continuing to appeal for sightings of the Nissan Terrano in the Christchurch area and between Christchurch and the West Coast on Saturday.
Sightings are also sought of Amy Farrall's white Toyota Corolla in the Woolston area on Saturday morning.
"A number of sightings have been reported to police by members of the public in the past 24 hours. Police are grateful for the assistance of those who have come forward with information,'' a statement said.
Anyone with information about the vehicles or any other aspects of the case is asked to contact Christchurch police on 03 363 7400 or anonymously through Crimestoppers on 0800 555 111.
Police are not seeking anyone else in the investigation.
Ms Farrall had been reported missing by an acquaintance on Saturday afternoon, but police said it was too early to say how or where she was killed.
Her distraught family released a statement yesterday, saying she was a kind and caring girl who loved animals.
She worked as a caregiver for Richmond Fellowship in Christchurch, and her family said she was always helping people in need.
"As a family we are devastated that her caring nature appears to have been tragically taken advantage of.''
