Our normal decision point for a bat to be considered legal is that the bat is labeled as ASA approved or USSSA approved with either a number or an official stamp. That being said, there are exceptions and we strongly urge all players and teams to check the official web sites for ASA and USSSA for the governing organizations interpretation and listings of approved bats.
Although our league operates with NSA affiliation, we do not follow their legal bat approvals as their policy is more lenient than either ASA or USSSA. We operate a recreational league with an important mandate to safety for all members.
One of the real challenges with legal bats appears to be a year to year variance in approval / non-approval. In the past, bats have been approved only to be changed to unapproved when subsequent testing occurs and discrepancies are found (eg: BPF rating is now found to exceed 1.20).