Property and business owners suing to stop the use of eminent domain for the $4 billion Atlantic Yards project are facing a crucial decision from a federal appeals court, one of the few remaining legal options for the opponents.

Yesterday, the opponents group argued that it deserves a trial to challenge the state’s taking of property for the project in the U.S. Court of Appeals for the Second Circuit. The appeal comes after a U.S. District Court judge in Brooklyn, Nicholas Garaufis, dismissed the plaintiffs’ lawsuit in June.

In arguments before a three-judge panel, the landowners’ attorney, Matthew Brinckerhoff, said that a trial was necessary to determine whether the state illegitimately awarded the project to developer Forest City Ratner, noting that a competing proposal brought more money to the state and did not require the use of eminent domain.

“The taking here was motivated by a desire to benefit a particular private developer,” Mr. Brinckerhoff said. The developer seeks to build a basketball arena and more than 6,000 apartments on a site near Downtown Brooklyn.

The state argued that allegations of motive are irrelevant since the public benefit of the project — a requirement for the use of eminent domain — was not in doubt. “The plaintiffs throughout this case confuse motive with purpose,” an attorney for the state, Preeta Bansal, said.

Should the appellate court rule in favor of the state, the opponents have only one avenue of appeal left to them: the U.S. Supreme Court, which hears only about 80 cases a year.