Here are the applicable laws:
Sec. 53a-217b. Possession of a weapon on school grounds: Class D felony. (a) A person is guilty of possession of a weapon on school grounds when, knowing that such person is not licensed or privileged to do so, such person possesses a firearm or deadly weapon, as defined in section 53a-3, (1) in or on the real property comprising a public or private elementary or secondary school, or (2) at a school-sponsored activity as defined in subsection (h) of section 10-233a.
(b) The provisions of subsection (a) of this section shall not apply to the otherwise lawful possession of a firearm (1) by a person for use in a program approved by school officials in or on such school property or at such school-sponsored activity, (2) by a person in accordance with an agreement entered into between school officials and such person or such person's employer, (3) by a peace officer, as defined in subdivision (9) of section 53a-3, while engaged in the performance of such peace officer's official duties, or (4) by a person while traversing such school property for the purpose of gaining access to public or private lands open to hunting or for other lawful purposes, provided such firearm is not loaded and the entry on such school property is permitted by the local or regional board of education.
29-28(e) 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.
Sec. 29-37. Penalties. (a) 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.
Sec. 29-38. Weapons in vehicles. Penalty. Exceptions. (a) Any person who knowingly has, in any vehicle owned, operated or occupied by such person, any weapon, any pistol or revolver for which a proper permit has not been issued as provided in section 29-28 or any machine gun which has not been registered as required by section 53-202, shall be fined not more than one thousand dollars or imprisoned not more than five years or both, and the presence of any such weapon, pistol or revolver, or machine gun in any vehicle shall be prima facie evidence of a violation of this section by the owner, operator and each occupant thereof. The word "weapon", as used in this section, means any BB. gun, any blackjack, any metal or brass knuckles, any police baton or nightstick, any dirk knife or switch knife, any knife having an automatic spring release device by which a blade is released from the handle, having a blade of over one and one-half inches in length, any stiletto, any knife the edged portion of the blade of which is four inches or more in length, any martial arts weapon or electronic defense weapon, as defined in section 53a-3, or any other dangerous or deadly weapon or instrument.