Looks like they do. It has been struck down in Florida and Missouri. Probably will in Tennessee as well. FWIW, less that 1% of welfare applicants in Tennessee have tested positive for drugs (of course, they're only tested for drugs if they admit to using drugs during their interview).
That's the stickler. I'm sure the State lawyers advised them of this clause.
IMHO, if they tested them all, a much higher percentage would test positive.