UPDATED: 12.32PM Residents of the usually quiet township of Seacliff near Dunedin believe a neighbourhood dispute may have led to yesterday's fatal shooting.

A 53-year-old woman was found dead at a property on Coast Road, near to where police earlier found a critically injured man.

It's understood the 59-year-old man had gunshot wounds when he was transported from Truby King Reserve to hospital yesterday morning.

A local resident told the Otago Daily Times the pair involved in the incident lived close to each other and would often argue.

They say you could hear them at the top of Coast Road screaming and shouting.

Police have recovered a gun, but they won't say whether it is connected to the two individuals, or whether the two individuals have links to each other.

A police cordon remains in place on Coast Road.

Police want to hear from anyone with knowledge of incidents in the Seacliff area over the past few weeks, as part of their investigation into the fatal shooting.

Police are yet to release the name of the woman, as they're still notifying family members.