I've always spelt that as "khazi" presumably by analogy with "khaki", and assumed it was probably Indian Army slang. However here's the current Wikipedia entry about the word:

"Lexicographer Eric Partridge derives khazi, also spelt karzy, kharsie or carzey, from a low Cockney word carsey originating in the late 19th century and meaning a privy. Carsey also referred to a den or brothel. It is presumably derived from the Italian casa for house, with the spelling influenced by its similar sound to khaki. Khazi is now most commonly used in the city of Liverpool in the UK, away from its cockney slang roots.

Which is interesting, and seems plausible enough (apart from the last sentecne, with its failure to recognize that the word isn't in general use all over the country.)