The expression "Search me". means "I don't know."
I, too have been unable to find out the origin of this expression, but it does seem to be used with this meaning in British English as well as American English. Here's the entry, for example,
"Something that you say when you do not know the answer to a question.:
"Where's Jack?" "Search me!"
it is quite common in INFORMAL spoken English. But I would not recommend using it in a formal business environment (e.g. in reply to a boss or in a meeting)