From The TimeSplitters Wiki

The baseball bat is first used in the mansion (and is the only place in the story game where you use it). It is better than using your fists, but dont waste your time.

Elite Yoshi's Tips

The Baseball bat is a close range combat weapon that will make sure your enemy is dead. It is a wooden bat, no, you can not put it on fire. Its good for close corners, better if you keep it as a back-up weapon.

For more tips, visit the Weapon tips page.