There is an O-Ring around the base of the mounting surface that rests against the fuel tank itself.
See Image
The "O-Ring' that you can see in the picture could be the point of failure.
If you want to be sure and rebuilt the petcock entirely and replace the vacuum valve diaphragm as well as the diaphram body O-Ring you can purchase one of these rebuilt kits specifically for you make, the image below is example.
If you google "2003 Kawasaki ninja ex500r petcock rebuild" you can see a few options to purchase. It's relatively simple just be wary of the spring shooting out of the diaphragm body as you disassemble it. Most kits are less than $20
Cheers and best of luck.