All this is possible during a side quest in the game when you use Franklin to find a weed stash. You only have very limited time to do this, so you should prepare: only when you are in the area and only during this side mission involving Barry you can do it!
The first 2 police cruiser are parked near the truck with the stash: a gray police cruiser will be parked in the back and a blue one behind it in the next alleyway. Simply go to the cruiser that you want, throw the people out of it and start your run (alternately, you can shoot them, but that gives you a three star wanted level and you have a helicopter to lose too!). Make sure to lose the cops and when the mission timer expires, do not retry the mission. Instead, continue the free roam mode and get your cruiser to the garage where you can safely store it.
And there you have it! Now you own an unmarked police cruiser in Grand Theft Auto (and you can own multiple ones actually if you simply do this over and over again!)