Kohler Courage SV470-610 18 HP Lawn Tractor

I couldn't find any break down of the carb but it looks like a basic carb.
 
You could have a sticky float needle or have some debris holding it open.
 
If your comfy pulling the carb off, removing and inspecting inside the float isn't terribly difficult.
 
If you have enough room, you can pull the bowl, still on the carb (Pinch off the fuel line, or turn gas off).  Try to catch what comes out (I use a small old/CLEAN tuna fish can) and check for any crap.
 
The carbs generally just don't start to leak gasket wise so I suspect the needle and seat to be dirty. 
 
If the inside of where the needle goes seems to be dirty(needle shows corrosion), an ear cleaner, cut down, metal cleaner applied to the tip.  Then attach to a drill motor and work it in and out.  Usually, it'll be filthy and take several tips to fully clean up.  You'll very likely have to pull the carb to do this.
 
Just flushing the bowl (R&R), may wash out any contaminates alone...
 
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Thanks for the input. I'll try cleaning out the bowl. I did find the model #, serial #, etc. Of the engine once I knew where to look. I'll try removing the bowl and clean float. If I remove carb, do I need a new gasket, or if the old isn't damaged, can it be reused?