The Connecticut "racial ridicule statute" (§ 53-37), first enacted in 1917, provides,

Any person who, by his advertisement, ridicules or holds up to contempt any person or class of persons, on account of the creed, religion, color, denomination, nationality or race of such person or class of persons, shall be guilty of a class D misdemeanor.

The statute is unconstitutional in three ways:

[1.] It restricts constitutionally protected speech based on its content and viewpoint—for instance, a political advertisement ridiculing or expressing contempt for Scientologists or conservative Christians or young-Earthers or jihadist Muslims or blacks or whites or any such group. There is no "hate speech" exception to the First Amendment, and there is no "ridiculing or contemptuous speech" exception.

[2.] The statute has in practice been applied to things that aren't "advertisement[s]" at all. I have found no prosecutions for advertisements that ridicule people based on race or religion—not for commercial advertisements (which in any event would be pretty bad for business these days) and not for political advertisements.

Rather, based on the 13 police reports that I read in 2018, prosecutors seem to be mostly enforcing the statute to punish people for race- or religion-based "fighting words": generally speaking, face-to-face personal insults that include racial or religious slurs. (The facts of the cases are a mix: Three involved racial insults of police officers, one case with anti-white insults and another with anti-black insults. The other ten mostly involved insults of black ordinary citizens, though one was of a Hispanic, one of someone perceived to be Muslim, and one of an ambiguously labeled "nigga cracker." The defendants were mostly whites, but two were likely Hispanic and one was black.) And of course most recently, in the University of Connecticut student case, two students have been prosecuted for shouting "nigger" while walking near dorms, but not addressing it to any particular student.

The law has thus been consistently used to prosecute (and convict) defendants that are not guilty of the crime they were charged with, given the plain text of the statute. And there are no appellate decisions reinterpreting the text of the statute (as there are for some statutes), so the defendants weren't guilty under either the law as written or the law as authoritatively construed. Indeed, the one nonprecedential decision I could find, National Socialist White People's Party v. Southern New England Telephone Co. (D. Mass. 1975) (3-judge court), and the one decision cited in that case, State v. Jensen (Conn. Cir. Ct. 1969), read the statute—consistently with its text—as genuinely limited to "advertisements." (The 1917 act that enacted the statute was titled "An Act concerning Discrimination at Places of Public Accommodation," and really was aimed at "advertisement[s]" for businesses, not at (say) speech during KKK rallies or the like.)

[3.] Even if the statute were somehow read as banning race- or religion-based fighting words—contrary to its text—there's a Supreme Court decision squarely holding such selective restrictions unconstitutional: R.A.V. v. City of St. Paul (1992). R.A.V. struck down a ban on those fighting words that "arouse[] anger, alarm or resentment in others" based on, among other things, race or religion; this statute seems to be read as a ban on those fighting words that "ridicule[] or hold[] up to contempt any person or class of persons" based on, race, religion, or nationality. The words of R.A.V. apply just as well to this statute: Even assuming that "all of the expression reached by the [statute] is proscribable under the 'fighting words' doctrine," the statute "is facially unconstitutional in that it prohibits otherwise permitted speech solely on the basis of the subjects the speech addresses."

Fortunately, some Connecticut legislators (such as state senator John Kissel) are taking their constitutional duties seriously, and suggesting that the law be repealed; the ACLU of Connecticut agrees (see this Hartford Courant article (Amanda Blanco)). But not the Connecticut Commission on Human Rights and Opportunities, which writes (and this is the only analysis it gives):

At a time when hate and bias incidents are on the rise [citing data], it is crucial that the state not remove these types of prohibitions that deter or punish this unacceptable behavior.

The CHRO also describes the law as "mak[ing] the ridicule of a person or group on account of creed, religion, color, denomination, nationality, race or class a class D misdemeanor," so the CHRO doesn't view the law as limited to "fighting words," but rather as covering "ridicule" more generally. Then again, the CHRO doesn't even mention the limitation to "advertisement[s]," and invents a prohibition on ridicule based on "class."

State representative Craig Fishbein also "said while he might support a modification of the statute, he would not support a full repeal":

"Free speech is not absolute," he said. "You can't just say anything." … Fishbein also shared concerns over the message repealing the law might send to the state. "I don't think it's appropriate," he said. "To repeal the statute would be in favor of the action [it prohibits]. It's troubling. … This conduct should not be adopted. Why should anybody ridicule?"

I would think that the Connecticut Legislature could find a way of communicating the message that (1) it is repealing an unconstitutional law because it has a duty to support the Constitution, (2) not everything that can be said should be said, and (3) not everything that shouldn't be said should be criminal. Indeed, I would think that this message is a pretty fundamental American principle.