From The TimeSplitters Wiki

The crossbow is a weapon found in the 1920's Aztec level in Timesplitters 2. It's arrows are of moderate strength and must be rapidly fired in order to kill an enemy. The arrows can be lit by torches (most notably in the Aztec level, or in Arcade level Mexican Mission) and can be used to set enemies on fire. In Story, the only way to kill a Wood Golem is with a flaming crossbow bolt. An arrow that has hit a wall or floor and has stuck in it can be picked up and reused, much like harpoons and traquilizer darts in Future Perfect.

This weapon is "replaced" by the Harpoon Gun in TimeSplitters Future Perfect.