Absent state law (and I doubt you will find any) It's a pure judgment call. If the garnishee is an owner on accounts in his own name and accounts owned jointly with others, I would take the individually owned accounts first. Then, I would go for joint accounts with a spouse, leaving joint accounts with others until last.
It's kind of difficult for someone to explain to a parent why their joint account vanished...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.