Green’s Dictionary of Slang

suffering an infestation of body lice or similar vermin.

1921		N&Q 12 Ser. IX 345: Cooty. Lousy; dirty.
1938		J. Curtis They Drive by Night 14: When your three planks got more than usually cooty you were supposed to write ‘bugs’ on them with chalk and leave them outside the cell-door.
1972		Galton & Simpson ‘Loathe Story’ Steptoe and Son [TV script] I thought he looked a bit cooty.
1979		(con. 1930s) J. Wolveridge He Don’t Know ‘A’ from a Bull’s Foot 4: When we got back we were cooty too.