Smell of Gas!

I just bought a used 1999 Oldsmobile 88 with only 31,000 miles on it. The car came from Ohio and has quite a bit of rust on the underneath. Supposedly the car belonged to a 94 year old woman that only drove to church and the grocery store. The car runs great and there are no check engine lights or anything on. When you drive the car, after you stop and get out, the smell of gas is really strong at the back of the car, or if you ride with the windows down you can smell it while driving. However, you cannot smell it inside if the windows are up. My dad checked and there are no any visible signs of anything leaking. Where is the smell coming from? With the windows down, it is strong enough to make you sick.