I know from personal experience that it's a good idea to turn the petcock off on a carbed bike. I bought a 250 Ninja that had a fully warm engine when I arrived to look at it. It ran OK when I tested it. Turned out that the carb bowl needles leaked enough to fill the crank case with fuel which ruined the engine. It was hard to start with a cold engine due to low compression.
Lesson not learned very well though because I don't turn it off on my current V Star 250. I checked the oil level several times right after I got it to make sure it doesn't leak.