ASA 7-6K and NCAA 11.14.1 both have the same exception to hitting the ball a second time. NFHS rules (2011) don't spell out the exception, but the case plays are consistent with the other rule sets.
ASA 7-6K EXCEPTION 2: When the batter drops the bat and the ball rolls against the bat in fair territory, and, in the umpire's judgement, there was no intent to interfere with the ball. EFFECT: The ball is live.
NCAA 11.14.1 EFFECT: If the bat is out of the batter?s hand(s) (on the ground), the ball rolls against the dropped bat in fair territory and, in the umpire?s judgment, there was no intent to interfere with the course of the ball, the ball is live. If it stops or is touched in fair territory, it is a fair ball. If the ball touches the dropped bat in fair territory and then rolls to foul ground and stops, it is a foul ball. If the ball rolls against the dropped bat in foul territory, it is a foul ball regardless.
If the bat is out of the batter?s hand(s) (dropped or thrown) and it hits the ball in fair territory, the ball is dead, the batter is out, and each base runner must return to the base legally occupied at the time of the pitch.
NFHS Case Plays (2011) - BAT HITS BALL A SECOND TIME: 7.4.13 SITUATION: B1 swings and (a) hits the ball which strikes home plate and bounces up hitting the bat while the batter is in the batter's box; (b) after laying down the bat and running to first, the ball hits the bat in fair territory; or (c) while advancing to first, drops the bat in fair territory and the bat, while still moving, hits the ball.
RULING: A foul ball in (a). The ball remains live in (b). In (c), the batter is out and the ball is dead.