Shirley tells the policemen they need a Search Warrant to look around the girls' apartment, but legally the men do not need one. Since the girls do not own the property, they have no authority to tell the policemen they need a Search Warrant. Only the Landlord or Landlady has the legal right to say that to Police.
At the end of this episode (which is supposed to be in early 1960), Squiggy refers to Mister Ed, but that show started in 1961.