OLR Report 2012-R-0463 explains why state law prohibits the carrying of electronic defense weapons but not handguns.
Under state law, electronic defense weapons, such as stun guns, are classified as dangerous or deadly weapons. With limited exceptions, the law prohibits people from carrying these weapons on their person or in motor vehicles (CGS §§ 53-206 & 29-38). On the other hand, handguns are not classified as dangerous or deadly and anyone who meets criteria specified in law can obtain a permit to carry them.
Nothing in the legislative history of PA 86-827, which added electronic defense weapons to the list of dangerous weapons, or PA 99-212, which banned the carrying of such weapons, indicates why the legislature thought that these weapons should be more stringently regulated than handguns. But part of the explanation may be that, under the Second Amendment to the U.S. Constitution, firearms have a degree of constitutional protection, which has been upheld by the U.S. Supreme Court. The Supreme Court has not ruled on whether stun guns are entitled to the same degree of constitutional protection as firearms. And we are not aware of any Connecticut court that has considered this issue. But the Michigan Court of Appeals, in a case not binding on Connecticut, has ruled that both the U.S. Constitution and Michigan Constitution protect a citizen's right to possess and carry stun guns for self-defense and the state may not completely prohibit their use by private citizens (Mich. Ct. App. June 26, 2012 (Docket No. 304293)).
For more information, read the full report.