I've never denied anyone permission to track an animal, but my general rule is you leave your weapon at the property line. If a person asks permission, I'll gladly help them track, recover, field dress, and drag out their animal. They can even use my cart if they need one. When it's all done, I'll shake their hand, congratulate them, and probably offer a bite to eat.
On the other hand, if someone decides to come on my land, get an attitude, tell me what he's going to do, and wave his gun in my face...I hope he finds his deer. By the time he drags it out, the game warden will be there to confiscate it and cite him for hunting without permission (that's what trespassing with a weapon gets you here), and the sheriff will be there to arrest him when I press charges for threatening me with a gun.
Be nice and ask, I'll do anything I can to help. Be a jerk, and your day is going to get a lot worse in a hurry.