No person may hunt deer or small game with a bow and arrow under the provisions of this chapter without a valid permit issued by the Commissioner of Energy and Environmental Protection pursuant to this section or § 26-86a for persons hunting deer with bow and arrow under private land deer permits issued free to qualifying landowners, or their husbands or wives, parents, grandparents, lineal descendants or siblings under that section. The fee for such bow and arrow permit to hunt deer and small game shall be forty-one dollars for residents and one hundred thirty-five dollars for nonresidents, or nineteen dollars for any person twelve years of age or older but under sixteen years of age, except that any nonresident who is an active full-time member of the armed forces, as defined in § 27-103, may purchase a bow and arrow permit to hunt deer and small game for the same fee as is charged a resident of the state. Permits to hunt with a bow and arrow under the provisions of this chapter shall be issued only to qualified applicants therefor by the Commissioner of Energy and Environmental Protection, in such form as said commissioner prescribes. Applications shall be made on forms furnished by the commissioner containing such information as he may require and all such application forms shall have printed thereon: “I declare under the penalties of false statement that the statements herein made by me are true and correct.” Any person who makes any material false statement on such application form shall be guilty of false statement and shall be subject to the penalties provided for false statement and said offense shall be deemed to have been committed in the town in which the applicant resides. No such application shall contain any material false statement. On and after January 1, 2002, permits to hunt with a bow and arrow under the provisions of this chapter shall be issued only to qualified applicants who have successfully completed the conservation education bow hunting course as specified in § 26-31 or an equivalent course in another state.