The battle for control over a prominent libertarian organization in Washington has cast a spotlight on its highly unusual structure, which allows the nonprofit research institution to be controlled by shareholders.

The Cato Institute, one of the largest think tanks in Washington, is governed by four people, each with a 25 percent stake in the organization. That stake can be bought and sold for cash under an arrangement, only legal in a handful of states, that is frowned upon by the Internal Revenue Service.

Charles and David Koch, billionaire brothers who own a large energy conglomerate, filed suit on Thursday seeking an option to increase their 50 percent stake in Cato, a large research organization that espouses free-market economics and limited government.

Charles Koch founded the organization with Cato president Ed Crane over 30 years ago. Uncommon provisions of law in Kansas have allowed the Kochs to remain firmly in control of the think tank, despite the fact that neither of the brothers have been major financial backers in years, according to Cato officials.

Although they don’t receive dividends like shareholders of a for-profit company, the structure gives the Koch brothers power to appoint half of Cato’s board. In most nonprofits, new directors are elected by the organization’s membership or the current board members.

“We think it’s a really bad structure,” said Robert Levy, Cato’s board chairman. “We’ve repeatedly asked that it be changed.”

Levy and Crane have accused the Koch brothers of mounting a “hostile takeover” with aims of using Cato to push partisan political goals instead of its current focus on policy.

Wes Edwards, a Koch lawyer, said the brothers filed the lawsuit as a last resort after offering mediation and a delay of the March 1 shareholders meeting. Charles Koch said in a statement that he doesn’t have a partisan agenda for Cato and simply wanted to make sure it “stays true to its fundamental principles.”

The unusual structure for Cato raises questions about whether it meets the requirements for a nonprofit under federal tax law since the board could essentially agree to allow control of the organization to be sold to the highest bidder — a highly unlikely scenario but one with possible legal ramifications.

“That is completely at odds with the requirements for [a nonprofit],” said Marcus Owens, a lawyer with Caplin & Drysdale in Washington. Owens was a lawyer with the IRS for 25 years and ran its nonprofit division for a decade.

“The Cato Institute is at risk of retroactive revocation of its tax-exempt status back to 1977,” Owens said.

If the IRS were to decide that Cato should not be exempt from federal taxes, it could order the organization to pay taxes on income from a limited number of years at the corporate rate of 35 percent. The organization had revenues of $39.3 million in 2011, according to its tax forms.

Cato’s lawyer on federal tax matters, Bruce Hopkins, agreed that the institute’s structure was very unusual and not favored by the IRS. However, he said there was no statute that prohibits the arrangement and that the restrictions put on the shareholders give them a “strange breed of stock that doesn’t have any economic advantage to it.”

“It’s a difference in form but that’s about it,” Hopkins said. “It is more of a control mechanism and in practice it’s not much different than a membership.”

The Koch lawsuit, filed in a Kansas county court, focuses on the fate of shares owned by former Cato chairman William Niskanen, who died in October. The Koch brothers contend in the lawsuit that the shares cannot be transferred to Niskanen’s widow without first being offered for purchase by the Cato board and the other shareholders.

Cato was incorporated without shareholders in 1974 with the name Charles Koch Foundation, according to Kansas records. In subsequent years, it was renamed to the Cato Institute and stock was given to a handful of individuals.

Under the terms of the agreement that governs Cato, if shareholders want to sell their stake in the organization, they would first have to offer the shares to Cato’s board for the same price they were acquired.

Three of the current shareholders bought their stake for only $16, according to the lawsuit.