Unlock costumes by completing the corresponding task.

Costume	How to unlock
Beat Cop Uniform	Complete the Cop missions.
Button Man - Carry extra ammo for all weapons	Complete the Badge Pursuit challenge.
Chicago Lighting	Link your game and account to Rockstar's Social Club. This costume enhances your accuracy with the BAR, Thompson, and the shotgun.
Golden Boy	Reach Traffic Desk.
Hawkshaw	Reach rank 18.
Sunset Strip	Reach rank 8.
Sword of Justice	Reach rank 3.
The Outsider	Reach rank 13.