HARTFORD, Conn. — When a Connecticut lawyer threatened to get a gun and shoot two water company workers if they didn’t get off his property, was it a crime or were his words protected by free speech rights?

That’s the key question in a case the state Supreme Court is scheduled to hear Tuesday.

Stratford attorney Laurence Parnoff, 75, was arrested on a misdemeanor disorderly conduct charge in July 2011 after he confronted two Aquarion Water Co. workers who had entered his property to conduct routine maintenance on a fire hydrant. The workers said someone had illegally tampered with the hydrant by removing its front cover, and police said it appeared Parnoff was using the hydrant to provide water for his goats.

Parnoff told the workers that they had no right to be on his property and threatened to get a gun and shoot them if they didn’t leave, according to the workers.

A jury convicted him in 2013 of disorderly conduct, but acquitted him of criminal mischief. A judge sentenced him to one year of probation and a $500 fine.

The state Appellate Court, however, overturned the conviction in 2015, saying Parnoff’s comments did not fall under the “fighting words” exception to free speech rights.

The court said “fighting words” must have a tendency to provoke imminent retaliatory acts of violence from the average person hearing the words. The court said potential violent retaliation was not imminent in Parnoff’s case, because there was no evidence he was carrying a gun and the statement was conditional on the workers not leaving the property.

State prosecutors disagreed with the ruling and appealed to the Supreme Court. Senior Assistant State’s Attorney Mitchell Brody, who will argue the state’s case, declined to comment on the appeal.

In court documents, Brody wrote that the average person would have been provoked into responding immediately and violently to prevent Parnoff from carrying out his threat and to retaliate against insults he also made.

“Guns are different; a threat to shoot a gun to resolve a dispute even more so,” Brody wrote. “They do not fit into ordinary discourse, however rancorous or intemperate. When injected into the verbal fray, they must be punished for what they are, fighting words spawning the likelihood of violence and disorderly conduct.”

Parnoff and his lawyer, Norman Pattis, did not return messages seeking comment.

Pattis wrote in a court document that Parnoff “contends that the jury disapproved of his speech and sought to punish him for it. Yet rudeness and mere belligerence alone do not violate the First Amendment.”

In July, the state Supreme Court ruled that a Vernon woman who was arrested after hurling a variety of insults at a grocery store manager was protected by free speech rights, because the insults were not “fighting words.”