Fuel leaking when running

[JPSmee]

Greetings folks, it's been a long time since I've been on here . . .

So, I decided to get my bike all set to get my state inspection done (it's been sitting in my garage for several months now, sadly being neglected). Once I got it running, I noticed that my bike suddenly started leaking fuel at a notable clip from the left side of the engine (when I cut the engine off, the leak ceased). I've only minor experience with these things, but it seems to me that a leak indicates that there is a seal problem. I've not done any carb work (or ever touched any seals for that matter) since I got it back in 2011.

Pic from above:
http://imgur.com/E4PctJA

I noticed that the leak seems to be moreso originating from the circled area:
http://imgur.com/IpMB5sw

I confirmed that the screw there is not lose. Out of abundance of caution with the fuel, I opted to not mess with it much while it was running.

[Re-run]

Well, a fuel leak is hard to trace as the fuel is so clear. Could be a couple areas. The bowl ring or drain screw not sealing around the threads. I would check the bowl ring first.  

The bowl isn't overfilling as then fuel would leak out the overflow tubes.

[shinyribs]

You've got a vacuum operated petcock, right? If so, when you stop the engine you stop the vacuum which could explain the connection. I would guess you might just have a typical bowl overflowing issue ( dirty or corroded needle and/or seat).