Does Left 4 Dead 2 Support Split-Screen Versus on Xbox 360?

No. Left 4 Dead 2 on Xbox 360 only supports split-screen in Campaign (co-op). Versus, Survival, Scavenge, and Realism modes are online-only.

To play Versus with a friend locally, you need two consoles, two copies, and two Xbox Live Gold subscriptions (System Link or online).