If the vacuum diaphragm in the petcock tears, gas will enter the carb and engine through the vacuum line, bypassing the float bowl...
You need to check the vacuum line for the presence of gas... There should be absolutely none... ZERO!...
That is the line going from the back of the petcock down to the right side of the carb, usually covered with a spring.
You find any gas at all in there, and you found the problem...
Chances are 100% there's gas in there.
Options are to replace with new, convert to manual, or replace with alternative (Yamaha Raptor 660 manual petcock. Convert is cheapest but most difficult, Raptor is easiest, stock replacement is easy but expensive.
http://www.ronayers.com/browseparts.cfm?SearchString=5LP-24500-01-00&adv=5&kw...
The Raptor is an easy bolt on fix. You will have to cap off the vac line at the carb. I put a screw in it.... rubber caps will rot away every couple of months and cause a vacuum leak.
As a bonus,... going to the Raptor makes tank removal much easier too. No more wiggle jiggle...