(Updated Sunday at 8:15 p.m.)A state trooper has filed a complaint with the Board of Labor Relations accusing the Connecticut State Police Union of denying him the right to know how union dues are spent.

The claim rests on case law that requires a non-union employee, who is nonetheless represented by the union in collective bargaining, to continue to pay a portion of their dues as a representation or agency fee. The law also requires the union to provide an explanation of how that money is spent.

The officer, Trooper First Class Marc Lamberty, made the complaint in late July following months of correspondence with the union’s president, Andrew Matthews. Lamberty resigned from the union in June 2011 in the midst of a vote by state employees on a concession package.

The police union was one of two state worker bargaining units to ultimately reject the deal. But in his letter asking to be removed from the union, Lamberty said his desire to resign predated the contentious concession package.

“Although it may seem a rash decision, especially in light of the ongoing [State Employee Bargaining Agent Coalition] vote, it was not. I have been considering my withdrawal for the past nine months and would rather withdrawal, then be a dues paying member who constantly complains about the CSPU,” he wrote.

In a return letter, Matthews accepted Lamberty’s resignation from the union, but informed him he would be required to pay 86 percent of the money he would have spent on membership dues as representation fees.

Lamberty responded that he was “rather taken aback by the 86 percent agency fee” and requested a calculation of the costs, as well as a verification of those costs by an independent accountant.

Matthews wrote back saying the union would try to get the information Lamberty had requested.

“We shall, hopefully within the coming week, forward you a summary of major categories of ‘chargeabIe’ and ‘non-chargeable’ expenditures, which expenditures have been verified by audit,” he wrote in late September.

Once he received the summary, Lamberty would have 30 days to challenge the union’s computations, Matthews said.

But about three months went by during which Lamberty said he had heard nothing back from the union about the summary. In early January, he wrote back to ask again.

“ln addition, your 30 day appeal process is quite absurd considering the 90+ days l’ve waited for a document that should be readily available. l question whether the 86 percent agency fee is completely arbitrary,” Lamberty wrote. “I am now demanding my dues be placed in escrow until this matter is resolved and I will take the same amount of time (90+ days) to review the document, if I ever get it, before making a further decision with regard to an appeal.”

That’s where the correspondence included with the complaint ends. The complaint, filed more than eight months later, goes on to accuse the union of engaging in prohibited practices by continuing to deduct fees from Lamberty’s pay without meeting its obligation to nonmembers.

Lamberty, who declined to discuss his reasons for leaving the union until after a hearing later this month, said Thursday he still hadn’t heard back from Matthews or anyone from the police union. He said the percentage of his dues the union is asking for seemed high, but he has no way of knowing whether that’s true without a breakdown of what they’re charging him for.

“I don’t have a problem paying an agency fee. I understand that this is closed shop state,” Lamberty said, adding that the union still negotiates benefits for him. But he said it’s his legal right to see a justification of that fee.

“I’m still waiting for [the document]. In my opinion if you have an agency fee, you should follow the law and come up with” how you arrived at the percentage, he said.

Reached Sunday, Matthews said the union was in the process getting an attorney to do a professional analysis of its fee breakdown. But he said a summary is made available annually.

Matthews said he would reserve comment on the complaint until the legal process had played out. But he said the union works hard to negotiate strong benefits for state troopers, who work a dangerous job.

“We don’t apologize for risking our lives and receiving the benefits we do,” Matthews said.