The ANZ documents were found in Armadale, in the city’s south-east, and included bank statements, personal details and private emails.
The information in the skip includes names, addresses, transaction histories and account numbers.
Legal experts wann the bank could be hit with a multi=million dollar fine.
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The documents were thrown out in a clean-up after the local ANZ branch closed its doors.
ANZ said it is “sorry this has occurred and is urgently investigating what happened”.
Watch the full story on 9News Perth at 6pm.