Our company needs to get a certificate of origin to ship overseas. For the authorized signature, can we use a notary republic of our local county?

The "rules" are made by the County you are shipping to.

What do they require? Are you asking if a local notary can "take" the signature of one of your employees?

I'm not sure what it is you want to know. I notary can only notarize a signature and would have nothing to do with authorizing anything.