I've seen that movie, but I really don't remember and tickling. In the movie, Newman was always flirting around with the maid. At one point, he got drunk and threw himself at her. Yes, Hud was a big a-hole.
But if there was any tickling, I bet Newman tickled the maid. It could've been in the movie, although I don't remember it.
Could you be thinking of "The Last Picture Show," another story written by the same person?