A post-mortem examination is due to be carried out today as police investigate the alleged murder of Invercargill woman Verity McLean by her police officer husband Ben.

Police say the results will be "factored into the ongoing investigation" of one of their own.

On Wednesday Invercargill police officer Ben McLean was charged with the murder of his wife, Verity, the mother of his three children - and the attempted murder of Garry Duggan, a man she was believed to be in a relationship with.

Police have this afternoon revealed more about the investigation into the alleged murder and attempted murder.

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"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.

"Three scenes of interest in Invercargill are currently being examined, including the property where the tragedy occurred, a park area at Inglewood Rd and Tweed St, and the defendant's residence on Scott St.

"Forensic staff are expected to complete an examination of the interior of the property on Otepuni Ave later today.

"They will then focus on the immediate area around the property.":

Basham said a number of separate investigative processes were ongoing.

"These include the criminal investigation which has oversight from of out-of-district police staff," he explained.

"Reports will also be prepared for any coronial inquiry, and an employment process has also begun."

The Independent Police Conduct Authority will also proactively oversee the police investigation.

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Basham said the families affected by the alleged incident were being supported by police and loved ones.

"Welfare staff are also working with police staff and their families who require assistance," he said

"We continue to appeal to the public for information which could assist the investigation."

Basham could not comment further on Verity McLean's death or what led to it.

"I reiterate that while police fully understands the high level of interest in this tragedy, our priority must be to protect the integrity of the investigation and the court process to come," he said.

"This means we are unable to discuss or confirm specific details about what happened, or details of the investigative steps we are taking.

"We are still in the early stages of the inquiry, and it will take time for us to build an accurate, verified picture of this tragedy."

Duggan remains in a stable condition in Southland Hospital.

Verity McLean and Ben McLean were living apart. Photo / Facebook
Verity McLean and Ben McLean were living apart. Photo / Facebook

McLean is also a patient at the same hospital.

He was remanded in custody after a special bedside court hearing yesterday but it is understood he is still being treated at the hospital.

A source told the Herald that Duggan was injured during a "struggle" with McLean at the time of the shooting.

The men have children who all appear to be friends.

It is understood the Duggan and McLean families know each other.

Duggan's wife Rachel told Fairfax that he, his lover and McLean were the only people who "know what was going on".

"No one else was there apart from Ben, Bert and Garry. It's their story to tell, not anyone else's."

Detectives and crime scene experts are back at the scene of the double shooting today.

Forensic specialists in white boiler suits are working at Otepuni Ave, where McLean and Duggan are said to have been living together.

Ballistics experts are also trying to piece together exactly what happened at the property on Tuesday night.

They can be seen coming and going from a white police tent erected outside the property in what is a largely industrial street.

Verity McLean's sister this morning declined to comment.

Private security remains at the McLeans' properties this morning.

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 is no longer registered as a teacher.

The Ministry of Education refused to comment on his teaching background.

"We would decline any employment records in relation to Ben McLean on the grounds of privacy," a ministry spokeswoman said.

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.