www.littleleague.org/learn/equipment/baseballbatinfo/batrules.htm

For age 12 & under baseball, only bats with the "USA Baseball" logo on them are legal for use.

For age 13 & up baseball, bats must have either the "USA Baseball" or "BBCOR" logos.

RULE 1.10 - SOFTBALL

1.10 - The bat must be a softball bat which meets Little League specifications and standards as noted in this rule. It shall be a smooth, rounded stick and made of wood or a material tested and proved acceptable to Little League standards. The bat shall be no more than 33 inches (34 inches for Junior/Senior/Big League) in length, not more than two and one-quarter (2-1/4) inches in diameter, and if wood, not less than fifteen-sixteenth (15/16) inches in diameter (7/8 inch for bats less than 30 inches) at its smallest part. Non-wood bats shall be printed with a BPF (bat performance factor) of 1.20. Bats may be taped or fitted with a sleeve for a distance not exceeding 16 inches from the small end. Colored bats are acceptable. A non-wood bat must have a grip of cork, tape or composition material, and must extend a minimum of 10 inches from the small end. Slippery tape or similar material is prohibited. 
An illegal or altered bat must be removed. 

NOTE 1: The traditional batting donut is not permissible.
NOTE 2: The bat may carry the mark “Little League Tee Ball.”
NOTE 3: Non-wood bats may develop dents from time to time. Bats that cannot pass through the approved Little League bat ring must be removed from play. The 2-1/4 inch bat ring must be used for bats in all softball divisions. Any bat that has been altered shall be removed from play.