Under Federal law a private residence can be restricted if any notice is given (verbal or posted sign), but that does not apply to private businesses.
I believe this is actually split between car and in-store. There is no federal law that prohibits me from giving you the boot from my store. I need not even give a reason. Just get out or be charged with trespass. However, I believe the gun may be kept in the car and that no employment policy may prohibit that.
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Fed HB2052 effective 7/1/13
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(a) Provided that the premises are conspicuously posted in accordance
with rules and regulations adopted by the attorney general as premises
where carrying a concealed handgun is prohibited, no license issued
pursuant to or recognized by this act shall authorize the licensee to carry a
concealed handgun into any building.
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(b) Nothing in this act shall be construed to prevent:
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(1) Any public or private employer from restricting or prohibiting by
personnel policies persons licensed under this act from carrying a
concealed handgun
while on the premises of the employer's business or
while engaged in the duties of the person's employment by the employer,
except that
no employer may prohibit possession of a handgun in a private
means of conveyance, even if parked on the employer's premises; or
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(2) any private business or city, county or political subdivision from
restricting or prohibiting persons licensed or recognized under this act
from carrying a concealed handgun within a building or buildings of such
entity, provided that the premises are posted in accordance with rules and
regulations adopted by the attorney general pursuant to subsection (f)
(h),as premises where carrying a concealed handgun is prohibited.