According to my records, it was September 5, 1970. He read the droppers before playing #40 on that show, and on every show I have listened to after that one from 1970 up through atleast the October 24th show (that's how far I've gotten so far.)
Well, he must have read them for a few weeks (or months or years) and then stopped, because I have several shows from the late 1970s in which he doesn't read the droppers. He wasn't yet doing it in 1982, either, because I remember someone mentioning when several songs fell out of the countdown from inside the Top Ten during late summer/early fall of that year, Casey didn't mention the droppers.
Yeah, I'll try to remember to let you know when I get to the next show that he does NOT read the droppers. I've listened to the January 22, 1972 show and I don't think he did on that one, so it's probably sometime in 71, but I dunno yet.