Also, does it make a difference whether the batter is in the batters box in this scenario?
Answer Brian, There are two different ways to look at this. 1) When the ball is hit, and the bat is dropped, and the ball rolls back and hits the bat, it is up to the judgment of the umpire if the batter tried to double hit the ball. If the umpire feels she did this, the ball becomes dead, and the batter is out. If he doesn’t feel like she interfered, the ball remains live. 2) When in the box, and the ball hits the bat a second time, the ball becomes dead. If the batter had a foot, or both feet COMPLETELY out of the batter’s box at the time of the second contact, the batter is out. If she was in the box, it is just a foul ball.