Although this specimen has 'S. Otago' as part of the location in 1938 Otago Land District covered most of the south of the South Island https://teara.govt.nz/en/interactive/17924/land-districts-1877-and-2008
There are two 'Centre Hill's in this area, one near Mossburn and one near Clinton, which are now both in Southland Land District.
PA Greer, Feb 2023