The lawsuit involves P&G's Herbal Essences logo and the design of the brand's bottles for shampoos and conditioners.
P&G claims that RNA is distributing shampoo and conditioner products under the name Hydrating Herbal Shampoo and Hydrating Herbal Conditioner, which infringe the Herbal Essences intellectual property rights.
The consumer goods giant wants RNA to be ordered to stop distributing the products, to recall existing inventory from store shelves and to destroy the bottle moulds.
P&G introduced the Herbal Essences packaging with the relaunch of the brand in 2006. It believes that RNA is selling the products in packages that copy Herbal Essences' packaging to capitalise on the brand's success and consumer loyalty.
P&G also claims that the unauthorised use of its 'trade dress' is likely to cause confusion and could jeopardise the goodwill that Herbal Essences has established among its consumers.
Steven Jemison, P&G chief legal officer, said: "We believe this is a clear case of infringement designed to take advantage of the Herbal Essences' business and its consumer loyalty.
"This is a serious case of intellectual property infringement and we are asking the court to stop the distribution of these products to protect the equity of Herbal Essences."