To unlock these cheat codes you have to first get an A grade on each level e.g. if you get an A grade on the 2nd mission you get the code "laser Law".
Taken from the Psxextreme.com cheats
Pursuit Force
Cheat Codes Go to the Cheat menu under Options and enter the following:
Laser Law - Police weapons shoot blue lasers, enemies shoot red
Double Damage - Activates Double Damage
Reoffender - Twice the loss on all negative Justice
Law Lord - Permanent, full Justice
Iron Man - Only half the health
Speed - Faster movement
Invincibility - God Mode
Open Road - No traffic
Wild Water - Permanent choppy water
Big Wheels - Wheels and Propelers increase in size
Sticky Feet - You cannot be thrown from vehicles
Time Trial Vehicles
Finish the appropriate mission in the Capelli series to unlock these cars in Time Trial: Hampton Avenger - Get an A on Rat Race
Hampton Monte Christo - Get an A on Rat Race
JME Marlin - Get an A on Cold Contract
JME Otter IV - Get an A on Witness Protection
KMT Seareaver - Get an A on Cold Contract
Zephyr ATS Law Enforcer - Get an A on Don on the Run