You need to use the overflow option, but with the following parameters:
.nav {
max-height:300px;
overflow-y:auto;
}
Use overflow-y:auto; so the scrollbar only appears when the content exceeds the maximum height.
If you use overflow-y:scroll, the scrollbar will always be visible - on all .nav - regardless if the content exceeds the maximum heigh or not.
Presumably you want something that adapts itself to the content rather then the the opposite.
Hope it may helpful