@Torrey
Well, that's why I say they should have to collide with you...it's strange to get busted just because they're on the same square as you.
@Kaiyodo
Actually, I don't think it would be a problem that they're driving a slidy car...basically, they'd be faster than you(Not much, but noticeably) and they could head straight towards you, but you'd have to use the slidy factor of the car to avoid them, i.e. you'd do a quick turn and they'd miss you and overshoot, then have to spin around and try getting you. Maybe even make them more slidy than your car is.
Also with them spinning around...I've seen them do that when it was a clear line of sight between them and me. Something with your pathfinding? If I remember correctly, the A* routine is very tile based, ja? So, the police only know which tile to head for and if they're on the same tile as you, you're caught? That's what it's looking like in here.
A bit of a suggestion. Cast a ray from police to player, see if it's colliding with any buildings. If it's not colliding, skip A* search. Have two vectors locked to the police car and offset to the sides, then one vector for player car. It can check the distance of the two vectors to the player vector, see which is the shortest and turn a little in that direction until they're both about equal. That was something I had done in a pathfinding routine, worked really well. If you get to the point of adding random traffic and collision between all the cars, I can post more of my pathfinding rountine. I think it would be a good compliment to A*, use A* to figure out which tile it needs to get to, but this other method to avoid hitting other cars.
And then, you can use Tokomak to make the other cars go spinning around when you hit them and then, you could.......okay, that's it. Next game I make is going to be a car game.
Too bad I'm all wrapped up in my fighting game right now.