Can You Play True Crime: New York City on Xbox 360?

No. True Crime: New York City (2005) was released on PlayStation 2, Xbox (Original), GameCube, and PC. It was never ported to Xbox 360.

Backward Compatibility?

• Xbox 360 BC List: The original Xbox version is NOT on the Xbox 360 Backward Compatibility list.
• Xbox One/Series X|S BC: Also NOT supported.

Related Title on 360

True Crime: Streets of LA (the predecessor) IS backward compatible on Xbox 360 (and Xbox One/Series X|S) via the original Xbox version.

How to Play NYC Today

• PC (GOG/Steam): Best version (widescreen, fixes, mods). Often on sale for ~$5-10.
• Original Xbox / PS2 / GameCube: Physical disc + working console.
• Emulation: PCSX2 (PS2), Dolphin (GC), Xemu (Xbox) — requires owning the game.