In Ohio Conceal carry license data in maintained in the "Law enforcement automated data system (LEADS)".
Chapter 4501:2-10 Law Enforcement Automated Data System (LEADS)
(W) "Law enforcement automated data system (LEADS)" means the statewide computerized network which provides computerized data and communications for criminal justice agencies within the state of Ohio. LEADS is administered by the Ohio state highway patrol superintendent. LEADS does not include data and files separately collected and maintained by intrastate regional systems or other individual user systems.
Other states do not have access to LEADS.
I don't know if Ohio enters this info into other databases, but I would bet they do. Review the above link and you will see all the other systems out there.
There is no such thing as privacy.