No guns signs
No guns signs do not have the force of law on private property. Failure to leave or disarm would only be trespassing. Banks and establishments that serve alcohol, which may be posted, are regulated separately. Hotel owners are prohibited by law from banning firearms, 70-24-110.
You may not carry a concealed firearm a in an establishment that serves alcohol on the premises (bars and restaurants), 45-8-328. It is illegal to carry a concealed firearm while under the influence of an intoxicating substance, 45-8-327. This does not apply to open carry, however many establishments are mistaken about the law.
Concealed carry is prohibited in a bank, credit union, savings and loan institution, etc. during normal business hours, except when using a drive-through, ATM, or depository, 45-8-328. This does not apply to mall or grocery stores with bank kiosks unless one goes into the actual banking area. This does not apply to open carry.
On open carry
"No gun" signs in Montana don't have the force of law regarding open carry. Like for anything else, if they don't want you to carry, the owner/operator has the right to ask you to leave, cover up, or disarm. If you don't, they can have you trespassed.
Reactions to open carry will be mixed. Very few businesses will be aware that they cannot legally ban open carry under the above statutes. Cops will likely be ignorant too.
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