He died intestate in 1960. Probate documents are available on Archway. NZ Government Archives.
Sources
Birth:https://www.bdmhistoricalrecords.dia.govt.nz New Zealand Births, Deaths & Marriages Online (Digital Database), Department of Internal Affairs] Birth Registration. Accessed 15 June 2023: 1904/4226 / Carson, William John/ Margaret & William
Marriage:https://www.bdmhistoricalrecords.dia.govt.nz New Zealand Births, Deaths & Marriages Online (Digital Database), Department of Internal Affairs] Marriage Registration. Accessed 15 June 2023: 1939/8648 Eva Theodora Connelly & William John Carson
Death:https://www.bdmhistoricalrecords.dia.govt.nz New Zealand Births, Deaths & Marriages Online (Digital Database), Department of Internal Affairs] Death Registration. Accessed 15 June 2023: 1960/35558 Carson William John 56Y
Burial: Find a Grave, database and images (https://www.findagrave.com/memorial/221574940/william-john-carson: accessed 23 June 2023), memorial page for William John Carson (1904–18 Nov 1960), Find a Grave Memorial ID 221574940, citing Karori Cemetery and Crematorium, Wellington, Wellington City, Wellington, New Zealand; Maintained by ! woowoo (contributor 49949980).