They can do anything they want to do until somebody stops them. Cities can prohibit CC in their buildings, if they pass the required ordinance. They can not prohibit OC. They can not prohibit any type of carry in open spaces. Is this a city building? Are they prohibiting CC, OC or both? Do the signs say "No Guns"(Weapons/Firearms) or do they say "No Concealed Weapons"? Is there any wording with the sign or just the "gun buster" circle/slash?
The two statutes that are relevant to this are KRS 237.115 and KRS 65.870. They can be read HERE and HERE.
I've looked at their website and this appears to be a city property. The City of Madisonville does have a "No Concealed Weapons" ordinance and it appears to be the proper ordinance. If they are prohibiting OC, they are committing a crime. Are the same signs on other city buildings? I'd bet that they will claim to only prohibit CC, or pretend to not know the difference between OC and CC, or at least claim not to. The best way to find out is to go in there OC and see what they do. Record the event, of course. Can you get pictures of the signs and any wording nearby?