1
general::
Phrase(s): have a screw loose [and] have a loose screw; have got a screw loose
Inf. Fig. to be silly or eccentric. • He’s sort of strange. I think he’s got a loose screw. • Yes, he has a screw loose somewhere. He wears a heavy jacket in the middle of summer.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Be mentally unstable or eccentric, as in Anyone who approves that purchase must have a screw loose. This term likens a mental weakness to a machine in which a part is not securely fastened. An antonym is have one's head screwed on right; for example, She's very capable; she has her head screwed on right. [Slang; early 1800s]
American Heritage Idioms