If it's a small puddle (as in the picture above)
and if the gas is coming from the hose at the bottom of the carb bowl, then the most likely cause is the o-ring on the carb float valve seat:
Replacing the o-ring is not difficult, but does take patience and care to do it without causing damage.
I do not wish to encourage you to do the job if you feel uncomfortable doing it.
There is the potential for breaking or losing parts during the process.
On the other hand, a dealer will charge a lot of $$$ to replace a 25 cent o-ring.
Here's the link to the manual. I believe the carb removal for the TK carb is in the supplement.
Manuals
http://tw200forum.com/index.php?/topic/75-service-and-repair-manuals/
Here's what's involved:
Remove the carb from the bike.
Remove the bowl from the bottom of the carb.
Remove the float, and the valve seat.
Replace the o-ring.
Then reassemble.
Also Yamaha will not sell just the o-ring. You have to purchase the valve, valve seat, and o-ring as a set.
I don't remember if you posted what year your TW is. If it's a 2001 or newer, I have extra o-rings. I don't know if they will fit the TW's before 2001.
If all this scares you, you can ride your TW the way it is, remembering to turn off the petcock every time your park.
jb