Here's Rule 1.10 for LL bats (Majors and below) - If your T-Ball bat meets these specifications, it's OK......(I'm going to assume it's not a composite bat, as that would require more info)
1.10 – The bat must be a baseball bat which meets Little League specifications and standards as noted in this rule. [SOFTBALL: 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 Softball 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.
Little League (Majors) and below: it shall not be more than thirty-three (33) inches in length nor more than two and one-quarter (2¼) inches in diameter. Non- wood bats shall be labeled with a BPF (bat performance factor) of 1.15 or less;