The Little League website has a page for Approved Composite Bats for Minors and Major Leagues that can be found here
. Majors and below use a 2 1/4" bat. If you are NOT using a composite bat, here is the list for approved non-wood bats
in PDF form which is updated regularly on Little League site, so download it again if it's been awhile since you last checked. It's possible your bat may not be on this list and still be perfectly fine for league play as long as it meets the criteria of rule 1.10 which is copied below for reference.
As of 1/2/2012, there are approximately 30 composite bats that are approved for play this season. Please check that list carefully if you're planning on using a composite bat in Minors or Majors this year. Umpires WILL be checking for illegal bats.
For Juniors level, you can check the list here
. Juniors use a 2 5/8" (or smaller) barrel bat.
The bat must be a baseball bat which meets Little League specifications and standards as notes in this rule. It shall be a smooth, rounded stick and made of wood or of material and color tested and proved acceptable to Little League standards.
Little League (Majors) and below:
It shall not be more than thirty-three (33) inches in length nor more than two and one-quarter (2 1/4) inches in diameter. Non-wood bats shall be printed with a BPF (bat performance factor) of 1.15 or less.
It shal not be more than 34 inches in length; nor more than 2 5/8 inches in diameter, and if wood, not less than fifteen-sixteenths (15/16) inches in diameter (7/8 inch for bats less than 30") at its smallest part.
In all divisions, wood bats may be taped or fitted with a sleeve for a distance not exceeding sixteen (16) inches (18 inches for Juniors) from the small end. 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 bat must be removed. Any bat that has been altered shall be removed from play.
Junior League: The 2 3/4 inch in diameter bat is not allowed in any division.
The traditional batting donut is not permissible.
The bat may carry the mark "Little League Tee Ball".
Non-wood bats may develop dents from time to time. Bats that cannot pass through the approved Little League bat ring for the appropriate division must be removed from play. The 2 1/4 inch bat ring must be used for bats in the Tee Ball, Minor and Major league baseball divisions. The 2 5/8 inch bat ring must be used for bats in the Junior division.