"Had there not been something crooked about Lizzie -- a screw loose, as people say -- she would never been within his reach." The Eustace Diamonds, Anthony Trollope, 1873.
Given the "as people say", perhaps this is an early use of the common phrase? I see no entry for "a screw loose" and just a couple comment references, so thought you might like this, and/or be able to supply more history. Thanks for a great site.