There is technically no property rights violation if you are lawfully armed and do nothing with you firearm on their property. Where is the state law?
It's not a violation of property laws, the problem is here in CT we must have a permit to OC or CC, even to purchase a handgun and the CGS say:
If you go into a place that is prohibited by the person in control of premises you are in violation of CGS 29-28 Subsection (e) which states, "The issuance of any permit to carry a pistol or revolver does not thereby authorize the possession or carrying of a pistol or revolver in any premises where the possession or carrying of a pistol or revolver is otherwise prohibited by law or is prohibited by the person who owns or exercises control over such premises."
Further reading shows CGS 29-37 States, "Any person violating any provision of section 29-28 or 29-31 shall be fined not more than five hundred dollars or imprisoned not more than three years or both, and any pistol or revolver found in the possession of any person in violation of any of said provisions shall be forfeited."
Notice the penalty for violating 29-28 is up to 3 years in jail, that makes this charge a felony, if found guilty you would be ineligible to own any firearms, never mind keep your permit. I have discussed this before with many people, the issue is CT does not mandate what kind of notice must be given, if there is not a clearly visible sign or no sign at all and you were charged with this you would have a great affirmative defense in court. But if you willfully pass a clearly marked sign I am sure you would be charged and either have to plea it down or wind up guilty of the charge under this statute.