Easy enough to test the petcock...
If it's a vacuum petcock, it should not allow fuel to flow if the engine isn't running.
Try draining the carb bowls with the petcock in the ON position. If fuel keeps on flowing after they should have emptied, the petcock is faulty.
Relevant threads (note: this is for a newgen model, so the part is different... but if it's vacuum operated, the principle behind the 2007 version is the same):
Discussion of symptoms
https://www.ninjette.org/forums/show...hlight=petcock
Solution, with pics of the petcock
https://www.ninjette.org/forums/show...hlight=petcock