When being chased by the police, open the GPS map and locate the nearest orange triangle with the pointer. Then, activate the GPS to show a blue arrow and lead you to the Pursuit Breaker. If the cops are directly behind you, they will stop because they "died". However, if you are at heat level 4 or higher, the cops (Corvettes) will just evade the debris. Once the cops have "died" it will then go into Cooldown mode. Then, just wait until you lose them. There is a quicker way to do this. If you go into GPS mode (after you have gone into Cooldown mode), there will be a blue-white dotted circle. Activate the GPS for the circle, then drive toward it and make sure that you are exactly in the middle of the circle. Your Cooldown meter should be drop down faster. After the little screen appears, you should be back to normal.
A muscle car or something just as good is recommended. Use it when the cops are really pestering you (especially the blue cars or Corvettes) and start to corner you against the wall. Enter slow time and crank it to the middle of the road to get free. This technique is also very helpful if you have a flat tire. It might be not as good, but it still may work.
When the police are looking for you but have yet to find you (when the map blinks red), back up against a wall. The cops will go past, but will not catch or see you. They will simply drive away.
To evade a pursuit with no tires. hit that Pursuit Breaker as soon as possible if you hit a spike strip during a pursuit but near a Pursuit Breaker. It should take out all the cars in the pursuit because they will be very close or all bunched together. Then, hide somewhere close by if possible.