You hold Shift down attempting to SMART over things...
... in every other game.
However, I actually did "free run" in most games before BRINK. It just did not work so well and didn't look so smooth.
Seriously, I was just shown the APB Reloaded Beta. A few missions in, I tried to SMART over a ledge.
If only it was possible! Games like APB desperately need to give players an optional ability for Parkour-movements.