The Mayor of Invercargill says the city is devastated by this week's double shooting.

Yesterday, Constable Benjamin Peter McLean was charged with the murder of his wife and the attempted murder of a man on Tuesday night.

Senior officers from outside Invercargill are leading the investigation - to make sure local police remain neutral.

Mayor Tim Shadbolt says he never met the woman, and doesn't know Constable McLean, but the couple had a lot of connections.

"We're of course shattered by this tragedy, and it affects so many people throughout the community, because everyone knows the people involved."

New Zealand Herald reporter Kurt Bayer said the case has rocked Invercargill's tight-knit community.

"Some locals that I've spoken to knew the Police constable. They are saying that they're absolutely shocked."

"Everyone is talking about it - it's the talk of the town."

Southern District Commander Superintendent Paul Basham said the priority for police is to remain impartial.

"We must also ensure that we protect the court process which is to come, and that the individual involved is afforded the same rights as any other member of the public."