hey let me start by giving you some background on my problem. i have a 97 bayou 300 4x4 that i am having the same problem with. atv runs perfect, but fuel running out of the overflow hose even with the petcock off. i took off fuel line from petcock and petcock will not shut off. i jacked with petcock for a minute and opted to order a new one. i bought a new petcock from bikebandit.com and replaced it. it cost me about 80 bucks...ridiculous. now my gas will shut off to carb i have had my carb apart at least twice trying to fix the overflow problem. Today i took entire carb apart and inspected needle valve and decided to order a new one...i am almost certain this will fix my problem. it has been very frustrating...i have done extensive research looking for the solution to my problem, which seems to be identical to yours. This is what i've found.
#1 check the drain screw on you carb located directly above the drain/overflow hose. i would suggest backing the screw all the way out and letting a decent amount of gas come out. catch it with some paper towels and pay attention if any trash comes out. There could be a piece of debris not fully allowing the drain screw to fully close. This is probably not your problem as it was not mine. I also replaced the screw since the allen head on my was almost stripped?! It wasnt because of me...previous owner i guess.
#2 You could have a leaking float...it could have a minute hole in it causing it to fill up with gas...This is also probably not your problem as it also was not mine.
#3 float height is not set correctly. I don't believe this is either of our problem since there I am almost certain there is no adjustment on these machines.
#4 Your needle valve and or seat is worn. I am almost certain this is both of our problems. I ordered a new valve from bikebandit.com...didn't shop around...probably should have. It cost 30 bucks...also ridiculous...i heard some people talking about getting aftermarket kits for around 15 bucks...but i personally prefer OEM. I just want this nightmare to be over and i'm tired of jacking with it.
This is the next step i would take if i were you. bite the bullet, order a new one, and change it out. The seat is pressed into the carb and i wouldn't have the slightest idea how to change it out. I wouldn't worry about this too much though because it is probably the rubber on the needle valve that is worn. I did hear some guy talking about using a wooden dowel to polish a seat but i personally am banking on the new needle valve fixing our problem. here is the link to the dowel procedure as well as more background on this specific problem...Reading This May Solve Your Leaking Carburetor Float Needle Valve And Seat Problems - Kawasaki Motorcycle Forums
I hope this helps
