A 50-year-old woman remains in a serious but stable condition at Dunedin Hospital, following a shooting in Invercargill last night.

Police have identified the 29-year-old man they believe is responsible, as Kevin Johnston.

His body was found by officers inside an Otatara Road house just after midnight.

Police say he appeared to have suffered from a self-inflicted injury and his death has been referred to the coroner.

There are reports the 50-year-old woman is his mother.

Police haven't confirmed that, saying only that the two were related.