Is it possible to play like, i will be a cop and chease my friend on lan game? There is no problem playing on lan but we want to play with police cars.

If it is not possible, any other game exist like this?

That would be cool. But i don't think you can. On the Playstation 2 version you can. There might be this option for Nintendo GameCube and Xbox 360 Live too, but for Computer i don't think so. :(