No, they didn’t.
It has only just been introduced and has yet to be voted on. An article published by The Huffington Post on January 18, 2011, “Kentucky Lawmaker: Drug Testing Welfare Recipients Would Save ‘Millions And Millions’,” describes the proposal of the bill (set forth by state representative Lonnie Napier (R-Lancaster) and cosponsored by House Speaker Greg Stumbo (D-Prestonsburg)), but does not describe the establishment of any law.
This page shows any current progress on the bill, and as of the very moment of this posting, it has only been introduced and nothing further.
A few statistics relating to recipients of public assistance and drug abuse can be found here.
Although it sounds like a pretty good idea in theory, it may conflict with Unwarranted Search/Seizure constitutionality. Also, the proposal is only about instituting a random drug testing format, rather than a mandatory testing for every applicant (which might be prohibitively expensive).
If you looked this up before you posted your Facebook status declaring your agreement with such a law, after seeing some other dimwit post it without even bothering to look it up, congratulations.
If you looked this up after you posted your Facebook status (or were directed here by someone with at least half a brain), please do not vote in any upcoming elections.