CASE,
a House, Shop, or Warehouse; also a Bawdy-house. As Toute the Case, view, mark, or eye the House or Shop. 'Tis all Bob; now let us dub the Gigg of the Case; now the Coast is clear, let us fall on, and break open the door of the House.
Case in the 1811 Vulgar Tongue
Also see examples in Canting Songs and Slang Rhymes collected by John S. Farmer (1896).