In 2009, a fan set up the page to salute Dean, but executors for the estate are claiming the use of the late actor's name and image constitutes a trademark violation.
CMG Worldwide CEO Mark Roesler tells ABC News: "We did not sanction the James Dean official Twitter account. There is no official Twitter site for James Dean because it's been misappropriated by an individual."
Bosses for CMG Worldwide are seeking unspecified damages in the lawsuit, which was filed in December in Hamilton Superior Court in Indiana.
Lawyers for Twitter are working to have the case moved to the US District Court for the Southern District of Indiana because of the potential amount of damages that could be awarded and the trademark infringement issues.
Dean was killed in a car crash in 1955.
