Lawyers for the star seek damages from Arcadia Group Brands Ltd., which owns the Topshop fashion chain, after it sold shirts bearing her picture without permission.
The shirts were initially sold as the "Rihanna Tank" and then — after she complained — as the "Headscarf Girl Tank" and the "Icon Tank."
Rihanna's lawyers accuse Topshop of trying to pass off the T-shirt as being approved or authorized by the singer.
The store says Rihanna is seeking legal recognition for a flawed assumption that "only a celebrity or her successors may ever market, or license the marketing, of her own character."
A hearing was held Friday.