casing (n.)

"enclose in a case," 1570s, from case (n.2). Related: Cased; casing.

The meaning "examine, inspect" (usually prior to robbing) is from 1915, American English slang, perhaps from the notion of giving a place a look on all sides. Compare technical case (v.) "cover the outside of a building with a different material" (1707), from case (n.) "external portion of a building" (1670s).