Both the new USA Baseball standard and BBCOR -3 ("drop 3") Bats are allowed (As well as wood).
For full details see the link for 2018 NBBL Rules on this page.
Bats rules are under VII - Equipment and Safety:
8. BAT REGULATIONS
All bats up to 2 5/8” barrel bats are permitted with no greater than a drop of 5. The bat shall not weigh, numerically, more than five ounces less than the length of the bat (e.g., a 33-inch-long bat cannot weigh less than 28 ounces). The bat MUST be USA certified and have the USA Bat Logo printed somewhere on the bat.
A simple rule of thumb is a bat may not exceed 2 5/8” barrel and no greater than a drop 5, the bat must have the USA Bat Logo printed on it.
Any drop 3 bats shall meet the Batted Ball Coefficient of Restitution (BBCOR) performance standard, and such bats shall be so labeled with a silkscreen or other permanent certification mark. The "BBCOR Certified .50" mark somewhere on their barrel or taper.
Additional requirements for a bat to become BBCOR Certified include a length to weight ratio that is no greater than -3 and a barrel diameter that does not exceed 2 5/8 inches.
Any composite should be no greater than a drop 3 and meet BBCOR standards.