Maid to Order (1931)

While trying to nab a gang of diamond smugglers, the police are notified by Scotland Yard that the gang's leader, a beautiful Englishwoman who was on her way to the States to take control of the gang, has been caught. Because the American gangsters don't know what their English boss looks like, the police persuade a female impersonator to pretend to be her and infiltrate the gang.