Apex domains cannot have CNAME records.
Question and response
Question
dig sth.nz. NS
Answer
sth.nz. 4 NS ns2.sth.nz.
sth.nz. 4 NS ns1.sth.nz.
Authority
The response has no authority records.
Additional
ns1.sth.nz. 4 A 58.84.37.183
ns2.sth.nz. 4 A 120.138.23.15
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0