As I have a similar interest in the police system to the OP, I have decided to post a few of my observations regarding the Ventura Bay Police Department (VBPD).
Firstly, the cars. There are two types of police cars used by the VBPD. The Ford Crown Victoria (“Patrol car”) is a commonly-encountered patrol unit, both mobile and stationary. They also appear at every heat level. The Dodge Charger SRT8 (“Highway Patrol unit”) appears in pursuits and can possibly be found in free-roam, and is faster than the Crown Victoria. As of the time of writing, I have not found a link between the heat level of a pursuit and the likelihood of Charger Highway Patrol units spawning. There are also supposedly special “Interceptor” versions of the two main police units, with all-blue lights and faster top speeds than the regular versions, although I have not been able to see them in action.
Next, the pursuit system itself. It appears that to initiate a pursuit, all one really needs to do is speed, drive recklessly or destroy public property. Such actions performed in view of a Patrol car is enough to get them to follow you. While a police unit is chasing you, you have the option to pull over as long as the fine is below $500. When stopped, press the L1/LS button (depending on console); the fine is deducted from your account and the police unit drives off. Once the fine rises above $500, the pursuit is formally initiated. If a police unit spots you while in a race, the pursuit is started automatically.
The heat level system is rather simple in its concept. The higher the heat level, the more units are dispatched, and the more aggressive the police will be in their attempts to stop you. The pursuit starts at Level 1, where a single Patrol car chases you, which should be easy enough to outrun. Once the fine reaches $1,500 (or thereabouts), the pursuit is upgraded to Level 2. Initially, pursuits only go up to Level 2.
Progressing through the Outlaw career path unlocks the next two heat levels. At Level 3, roadblocks are set up. These come in two varieties. The smashable roadblocks consist of simply a line of sawhorses across the road, with blue flashing lights. These slow you down, but can be broken through. Reinforced roadblocks consist of steel barriers and a few police vans. These roadblocks should be treated like the SWAT roadblocks in 2012’s Most Wanted: impassable. Any attempt to break through this kind of roadblock will see your car stop dead, and leave you vulnerable to following police units. It is recommended to find an alternate route instead.
At Level 4, spike strips are set up. These should be self-explanatory by now; running over a spike strip bursts your tires and makes escape almost impossible. Luckily, these spike strips should be easy to spot, as they are accompanied by red flashing lights and are only laid out across half the road. Interestingly, it may actually be possible for a Patrol car or Highway Patrol unit to run over their own spike strip and be taken out of the pursuit. There is also a Heat Level 5, which as far as I can tell is more of the same.
Should you find yourself stopped, with police units close by, you should attempt to get moving by any means necessary. If you cannot escape before the camera fully zooms out, you will be busted. The fine accumulated during the pursuit will be deducted from your account, and you will (presumably) respawn at the nearest garage. I shouldn’t have to tell you that getting busted should be avoided at all costs, even though your car will not get impounded. Take note that moving off before you are busted counts as Resisting Arrest, and your heat level will increase to the next level.
As for evading the police, it is pretty simple. You need to break their line of sight. If you have a high-powered car, it can be as simple as getting on a highway and accelerating away. The Crown Victoria Patrol car has a maximum speed of 120mph, which should be easy enough for even a moderately-tuned streetcar to exceed. The Highway Patrol Chargers are faster, topping out at around 160mph, which makes outrunning them harder, but not impossible. If find yourself in the city, then you should make sharp turns to lose the police. They do not seem to be able to take corners very well, so use the alleyways, back streets and other tight sections of Ventura Bay to your advantage.
Once line of sight has been broken, you will enter the Cooldown phase. A timer will count down, indicating how long you have left to lose the pursuit. This timer lasts for just 10 seconds at Level 1, while you will need to hide for 30 seconds at Level 5. While in this phase, the police will still be searching for you, and being spotted by a police unit or roadblock will re-initiate the pursuit. A tactic to increase the chances of remaining hidden is to stop and turn off your engine by pressing the O/B button. This will also cut the lights, and will make it harder for the police to spot you. For maximum effect, it is recommended to park down an alleyway, side street, or basically anywhere away from the main road, and turn off your engine. This makes it very hard for the police to spot and recognize you, and makes it very likely that you will escape.
Once you escape, the rep gained from the police evasion will be added to your total. Be warned that any heat level gained from a pursuit seems to be carried over. For example, if you evade a Level 3 pursuit, your next pursuit will start at Level 3. It remains to be seen whether the police will automatically initiate pursuit at high heat levels. Finally, (I assume, though I am not 100% sure) swapping cars in your garage will cancel the heat level gained.
I have made these observations through watching gameplay videos on YouTube, as well as noting comments made by other users on GTPlanet. However, there are still a few things I am not sure of, and will have to wait until I get a copy of Need For Speed for myself to experiment and make sense of how the VBPD operates.
... Which was ridiculous. I swear the crown vic's had 800HP or something.
