Call of Duty: World at War (Wii) — No Local Multiplayer

Call of Duty: World at War on Wii does not support split-screen or any form of local multiplayer. Multiplayer is online-only via Nintendo Wi-Fi Connection (now defunct, though community servers like Wiimmfi exist).

Wii CoD Games That Do Have Split-Screen

• Call of Duty 3 (2006) — 2-player split-screen offline
• Call of Duty: Modern Warfare Reflex (2009) — 2-player split-screen offline

If you're looking for couch co-op or versus on Wii, those two are your only options in the CoD series. World at War on Wii is a solid port with pointer controls, but it's strictly a single-player/online experience locally.