A little coolant leaking...???

[1hot5.0]

As you all probably know, I just got my car. I noticed, however, that if I start my car and drive it, it will leak no coolant and will run at the temerature it should. When I turn the car off, after about a minute, it will start leaking coolant for about a minute. It will then stop. But the next time I turn off the car, it does the same thing. I looked at it with a friend, and we both think that it is coming from a loose hose near the overflow tank. Is this normal for 5.0's? I thought it was never good if your car leaked coolant.