Apex domains cannot have CNAME records.
Question and response
Question
dig state.nc.us. NS
Answer
state.nc.us. 5 NS ns1.nc.gov.
state.nc.us. 5 NS ns2.nc.gov.
Authority
The response has no authority records.
Additional
ns1.nc.gov. 5 A 149.168.11.11
ns2.nc.gov. 5 A 149.168.138.11
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0