So it would appear that the hospital is the same as any other privately owned store/restaurant. Signs don't carry weight until asked to leave (except those on areas listed in section 16).
(16) Except as provided in KRS 527.020, no license issued pursuant to this section shall authorize any person to carry a concealed firearm into: (a) Any police station or sheriff's office; (b) Any detention facility, prison, or jail; (c) Any courthouse, solely occupied by the Court of Justice courtroom, or court proceeding; (d) Any meeting of the governing body of a county, municipality, or special district; or any meeting of the General Assembly or a committee of the General Assembly, except that nothing in this section shall preclude a member of the body, holding a concealed deadly weapon license, from carrying a concealed deadly weapon at a meeting of the body of which he or she is a member; (e) Any portion of an establishment licensed to dispense beer or alcoholic beverages for consumption on the premises, which portion of the establishment is primarily devoted to that purpose;
(f) Any elementary or secondary school facility without the consent of school authorities as provided in KRS 527.070, any child-caring facility as defined in KRS 199.011, any day-care center as defined in KRS 199.894, or any certified family child-care home as defined in KRS 199.8982, except however, any owner of a certified child-care home may carry a concealed firearm into the owner's residence used as a certified child-care home; (g) An area of an airport to which access is controlled by the inspection of persons and property; or (h) Any place where the carrying of firearms is prohibited by federal law.
(17) The owner, business or commercial lessee, or manager of a private business enterprise, day-care center as defined in KRS 199.894 or certified or licensed family child-care home as defined in KRS 199.8982, or a health-care facility licensed under KRS Chapter 216B, except facilities renting or leasing housing, may prohibit persons holding concealed deadly weapon licenses from carrying concealed deadly weapons on the premises and may prohibit employees, not authorized by the employer, holding concealed deadly weapons licenses from carrying concealed deadly weapons on the property of the employer. If the building or the premises are open to the public, the employer or business enterprise shall post signs on or about the premises if carrying concealed weapons is prohibited. Possession of weapons, or ammunition, or both in a vehicle on the premises shall not be a criminal offense so long as the weapons, or ammunition, or both are not removed from the vehicle or brandished while the vehicle is on the premises. A private but not a public employer may prohibit employees or other persons holding a concealed deadly weapons license from carrying concealed deadly weapons, or ammunition, or both in vehicles owned by the employer, but may not prohibit employees or other persons holding a concealed deadly weapons license from carrying concealed deadly weapons, or ammunition, or both in vehicles owned by the employee, except that the Justice and Public Safety Cabinet may prohibit an employee from carrying any weapons, or ammunition, or both other than the weapons, or ammunition, or both issued or authorized to be used by the employee of the cabinet, in a vehicle while transporting persons under the employee's supervision or jurisdiction. Carrying of a concealed weapon, or ammunition, or both in a location specified in this subsection by a license holder shall not be a criminal act but may subject the person to denial from the premises or removal from the premises, and, if an employee of an employer, disciplinary measures by the employer.