The families of the Anzac Day shooting victims are "shocked" by events and are rallying around as they try and cope with the tragedy.
Verity Ann McLean, 40, also known by the nickname "Bert", was allegedly murdered by her police officer husband, Ben McLean.
He has also been charged with the attempted murder of Garry Duggan.
The McLeans, who have three children, separated about a month ago, the Herald has been told.
Duggan, it's understood, was also separated from his partner and had been living with Verity McLean at the Otepuni Ave property where the alleged shooting took place shortly after 8pm on Tuesday.
A statement from the family of Verity McLean, whose maiden name was Barber, was released through police media today.
"We, as the family of Ben and Verity McLean, acknowledge the tragic circumstances following the events of Tuesday night in Invercargill," said family spokeswoman Jane Allan.
"We are all very shocked and are trying to cope with what has happened as best we can as a family."
The family thanked the Invercargill community for its outpouring of support and compassion, as well as police for the "very difficult job they have to do" along with St John Ambulance, hospital staff and Victim Support.
"We have been overwhelmed by kindness and understanding, from family, friends and people within the community, some of whom we have never met," Allan said.
The family has now asked for privacy.
McLean and Duggan both remain in Southland Hospital.
Duggan suffered a fractured skull while allegedly struggling with McLean, the Herald has been told.
A post-mortem examination was due to be carried out today. The results will be "factored into the ongoing investigation" of one of their own, police said.
"The investigation is continuing, with a team of detectives and specialist forensic staff working to piece together the tragic events of Tuesday night," said Southern District Commander Superintendent Paul Basham.
There are three "scenes of interest" currently being examined, including the property where the shooting occurred, Tweed St Playground about 200m away, and McLean's residence at Scott St just outside of town.
Forensic staff were expected to complete an examination of the interior of the Otepuni Ave property, located in an industrial area, today.
"They will then focus on the immediate area around the property," Basham said.
A number of separate investigative processes are ongoing, including the criminal investigation which has oversight of out-of-district police staff and from which reports will also be prepared for any coronial inquiry. An employment process is also under way, while the Independent Police Conduct Authority (IPCA) will "proactively oversee" the police investigation.
It is understood the Duggan and McLean families know each other.
A McLean family friend today told the Herald that everybody is in "total shock".
"There's actually not a word in the English language to sum it up: tragic, stunned, shock... they just don't quite cover it," they said.
"What sucks is the people closest to them can't make head nor tails or it.
"This is nothing like anyone down here has ever dealt with before. It's incredibly hard for everybody.
"Whatever has happened, poor Bert did not deserve this."
The Herald understands that McLean was a teacher before he joined police about 10 years ago.
He taught science at a Southland high school but was no longer registered.
The Ministry of Education refused to comment on his teaching background.
Former students have expressed their shock at the arrest of McLean, who was popular during his time teaching.
"He was one of the best," one ex-student said on Facebook.
"He was the cool teacher," another added.
Do you have information?
This can be provided directly to Invercargill police on 03 211 0400.
Alternatively, people can call Crimestoppers anonymously on 0800 555 111.