While some CLEOs treat the signature as "giving permission", it really only says there is no legal reason not to issue the license or tax stamp. I don't know of any CLEO who will furnish a copy of the law or give any advice to an applicant, they will just approve or disapprove.
The CLEO does not get any opportunity to approve or not approve a C&R license. You send them a copy. They can do what they will with it, but they get no say in whether it is issued or not.
Disclaimers: I am not a lawyer, cop, soldier, gunsmith, politician, plumber, electrician, or a professional practitioner of many of the other things I comment on in this forum.