Public school context
Many courts would likely evaluate such cases using the “plainly offensive” standard established in Bethel School District No. 403 v. Fraser. In Fraser, the U.S. Supreme Court ruled that public school officials could punish a high school student for delivering a speech containing sexual innuendos to the student body. The Court reasoned that “it is a highly appropriate function of public school education to prohibit the use of vulgar and offensive terms in public discourse.” These words gave rise to the “plainly offensive” standard that many courts use in examining messages on T-shirts.

There have been no cases directly ruling on a T-shirt that reads “Kill A Cop,” but there have been various other cases relating to messages on T-shirts. In 2000, the 6th U.S. Circuit Court of Appeals ruled in Boroff v. Van Wert City Board of Education that a student’s T-shirt was plainly offensive by promoting “disruptive and demoralizing values.” Nicholas Boroff's T-shirt featured musician Marilyn Manson with a three-faced Jesus and read “See No Truth. Hear No Truth. Speak No Truth” followed by the word "BELIEVE" with the letters "LIE" highlighted. In this case, the public school officials won because the court found the shirt to be “plainly offensive.”

“Plainly offensive” has been interpreted differently by other courts. For example, the 2nd Circuit in 2006 ruled in Guiles v. Marineau that Vermont school officials violated a student’s First Amendment right by punishing him for his T-shirt that referred to President Bush as "Chicken-Hawk-in-Chief" and included text and drawings alluding to his alleged past drug and alcohol abuse. Using the Fraser standard, the court found that Zachary Guiles' shirt was not “plainly offensive.”

Typically, the more political a message is, the more First Amendment protection it is granted. This was the case in the landmark 1969 ruling Tinker v. Des Moines Independent Community School Dist. The U.S. Supreme Court ruled that public school students could wear black armbands to school to protest U.S. involvement in the Vietnam War. The Court noted that the students were engaging in a form of symbolic speech that was “akin to pure speech.” In later decisions, courts have recognized that students have more protection when they engage in political speech, whether that expression is on a T-shirt or otherwise articulated.

On the other end of the spectrum, in 1992 a federal court denied a Virginia student’s First Amendment claim that she should not be punished for wearing a “Drugs Suck” T-shirt to class. Even though the message on Kimberly Broussard's shirt spoke to an important political topic, the court determined that the word “suck” was too vulgar and could be prohibited as being plainly offensive under the Fraser standard.

A court would likely side with a school that disciplined a student for wearing a shirt that read “Kill A Cop” because such language would be determined to be “plainly offensive” under the Fraser standard.

Other contexts
Outside the public-school context, a government official would have to believe that the message on a person's T-shirt constituted some sort of true threat or fighting words in order to demand that the shirt be covered up or removed.

The U.S. Supreme Court ruled in the 1942 ruling Chaplinsky v. New Hampshire that “fighting words”— words “which by their very utterance inflict injury or tend to incite an immediate breach of the peace” — are prohibited and unprotected by the First Amendment.

Another form of speech that is not protected under the First Amendment is a “true threat.” The courts have defined a “true threat” as a threat which involves statements with serious expressions of intent to commit an act of violence to an individual or group of individuals. The Supreme Court in its 1969 ruling Watts v. U.S. also labeled a “true threat” as a real threat to one’s personal safety.

In 2003, an interesting case came out of Michigan's Court of Appeals regarding a courtroom spectator. Henry Dudzinski was ordered in contempt of court for failing to remove his T-shirt after the judge asked him multiple times to do so. The T-shirt read “Kourts Kops Krooks.” The judge found that the shirts “affected the fair administration of justice.” Dudzinski served a 29-day jail sentence.

In another extraordinary case, Venus “Star” Morgan, a 21-year-old Murray State University student, was issued a harassment citation by the police for wearing a T-shirt to a public festival which depicted Marilyn Manson and this phrase: "I Am The God of F***" from the song, "White Trash." In 2001, the Kentucky Court of Appeals ruled that the statute used to convict Morgan defines harassment as conduct as opposed to speech, and the panel of judges held that wearing the T-shirt could not be considered a form of conduct. Since the case was decided upon as conduct, and not as speech, it is not strictly a First Amendment free-speech case.