Ernesto, it looks more like a float problem. The float level in the bowl may be too high. You can adjust the needle clip as needed to correct this. Also if the carb is attached at an angle (and not level itself), rotating the float bowl may change its height relative to the main body, as some have suggested above.
The overflow in your video doesn’t appear to be from a “leak.” There is an overflow outlet in the main body of the carb (toward the bottom—in your video, it’s the hole just above the silver ring below the main body) to allow petrol to escape if the level is too high. This is to prevent flooding of the main body and the air intake if the float malfunctions, say.
After I tickle my carb on my Comet, some petrol will escape from the overflow. Once the bike starts running this will (should) cease and it shouldn’t begin again after you’ve stopped and cut the engine. So, I think it’s just an issue with the float—either just too high, or the float isn’t properly closing off the fuel supply when it rises.