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(ABC NEWS)-- Famed jeweler Tiffany and Company is suing warehouse store giant Costco, claiming it sold knockoff engagement rings falsely labeled as "Tiffany."

Tiffany alleged trademark infringement, counterfeiting, deceptive business practice, and false advertising. It's also suing for injury to business reputation, saying a customer informed them in November that she was "disappointed" that she saw Tiffany diamond engagement rings at a Costco store in Huntington Beach, Calif.

Costco, based in Issaquah, Wash., and Tiffany & Co., the holding company for principal subsidiary Tiffany and Company based in New York City, did not return requests seeking comment.

Tiffany filed the lawsuit in U.S. District Court in New York on Thursday.

Jeffrey Mitchell, attorney for Tiffany, said hundreds if not thousands of Costco members may have mistakenly believed they were buying Tiffany rings.

"One of the reasons to file the lawsuit is to get all the information about what was going on at Costco, how long and why," he said. "The lawsuit will hopefully answer those questions.

When asked if Costco customers who may have been duped will ask for a refund, Mitchell said, "That's between Costco and its customers how they will deal with that."

Costco has been the subject of lawsuits by retail companies, including Calvin Klein, for allegedly hurting higher-end brand names by selling products at low prices.

Leigh Ann Lindquist, attorney with Sughrue Mion, PLLC, a law firm that is not involved in this dispute, said Tiffany wants to maintain control over its name and products.

"It wants consumers to come to its store or website to purchase product which are known for their quality," she said. "Going to a Tiffany store is an experience and walking away with a blue box with a Tiffany ring is something special that Tiffany created."

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