Baldwin sued the Dances With Wolves star in December, claiming he should have benefited from Costner's success after he introduced an oil-filtration device to help clean up the Gulf of Mexico oil spill last year.
BP bosses reportedly invested more than $50 million in the gadget, pioneered by Costner and his inventor brother. Baldwin is demanding more than $4 million from the actor, but Costner has filed to dismiss the legal action.
In a motion filed earlier this month, Costner insists he played no official role within the company in distributing the machines. He also argues that The Usual Suspects star Baldwin has inadequately provided any proof of how Costner duped him into selling his shares.
Costner's filing states: "Plaintiffs fail to allege facts that attribute even a single untrue statement made by Costner, fail to allege facts from which the Court can infer that Costner intended to deceive or mislead the Plaintiffs, and fail to set forth any facts demonstrating that Plaintiffs actually relied on any false or misleading statement made by Costner."