THROWING THE BAT RULE
There is no rule that covers this situation. It is a safety issue and may be handled under the authority of rule 9.01(c) which gives the umpire authority to rule on anything not specifically covered in the rules.
Hudsonville Little League house rule for throwing of a bat:
After the first occurrence, a warning will be issued to the player and the manager that if he/she or any other player lets go of the bat again, he will be removed from the game. He/she may remain on the bench, he just can't play anymore in that game. The place in the batting order is just skipped, no out awarded. If the player removed from the game causes the team to have fewer than 9 players in the field, the offending player(s) may be used on defense; but are removed from the batting order for the remainder of the game. This is NOT an ejection subject to game suspensions, unless it is a malicious act determined by the umpire under rule 9.01(c).