Late last month, the Connecticut think tank of which I am chairman was the subject of a bizarre complaint filed by public-union leaders. Their gripe? That the Yankee Institute is critical of union practices and that our funders share the same view.

Since last year’s election, every statewide office is now held by Democrats who support public unions. Possibly intoxicated by this success, public-union leaders filed this baseless complaint with the state’s attorney general, in effect asking: Will no one rid us of this meddlesome think tank?

The first enumerated “fact” in the complaint states that the Yankee Institute “is funded in part by, and connected to, such ‘think tanks’ as The Heritage Foundation, and the Cato Institute and by billionaires such as the Koch brothers.”

Putting aside that this isn’t true—although, believe me, we would like to become connected to the Koch brothers—why would the fact that we associate with like-minded people and institutions be of interest to a law-enforcement official? That is our right, plainly protected by the First Amendment of the Constitution.

Further down in the complaint, the union leaders arrive at another problem they have with us: They disagree with our political views. The complaint describes the Yankee Institute as “dedicated to the elimination of collective bargaining.” Then they allege that we have advocated for “moving their work to private employers.”

Well, OK, at least those last two points are close to the truth. We believe union dues are recycled into political activity, giving the union leaders huge influence over state and local elections. This allows public-union leaders, in effect, to choose their bosses. For that reason, they can extract much greater pay and benefits from the taxpayers than they should. It’s also true that we believe the private sector could do many jobs better and for less money than the government.

As for the rest of the complaint, if you had the patience to read all the way down to the end you would see that they also claim that we interfered with labor negotiations by hacking into the state computer system. Never mind that the charge had no shred of evidence. At least it would have been an actual crime.

Although I was pretty certain that Yankee was neither clever enough, nor technologically proficient enough, to have hacked anything, if the union did have any information showing otherwise I wanted to know. So Yankee asked the union leaders to provide some proof of their allegations or apologize. They did neither. When members of the media asked a union spokesman about our demands for proof or an apology, he replied that “Yankee Institute is the one who should be doing the apologizing for attacking working people.”

Let me pause and note that we’re trying to help the vast majority of Connecticut’s workers—those in the private sector who pay the third-highest per-capita taxes in the country to fund extraordinary benefits for public workers. These workers enjoy benefits that are not available to any but the most fortunate private-sector workers.

Pressed for further comment, one union spokesman responded with a veiled threat of force: “Does [Yankee] really want Wisconsin in Connecticut?”

So where’s the outrage? The most powerful special-interest group in the state files a complaint with a law enforcement official challenging our First Amendment rights and making criminal allegations without evidence—and elected officials respond with a collective shrug.

Mr. Cowin is chairman of Yankee Institute, a state think tank based at Trinity College