Bat dropped in fair territory

[Cindylou]

Please correct me if im wrong, but I am under the assumption that if the bat is rolling (moving) and hits the ball in fair territory, the ball is dead and the batter runner is out. But, If the ball hits the bat and the bat is stationary the batter runner is not out.

But I still would like clarification as to whether the bat "MUST BE" dropped in foul or it does not matter??

Cindy