If I'm understanding you correctly----then yes, there is a vent tube right next to the fill tube where you fill the tank.
When I fill my tank, I can hear and feel air rushing back out the vent tube. If I over fill the tank, it will puke the excess water out the vent tube.
Not really recommended to fill fast, or to let it over fill.
On my old camper I actually had a hose that came out the bottom of the unit and if I over filled it would drain the excess water.
The reason I am asking is that after I filled for the first time, I notice some water dripping from the frame where the underbelly was attached. This was right below where the fill tube is? Any idea what may have caused that?
Maybe either the fill tube, or the vent tube is loose where it connects to the tank. I don't think there is a positive way of telling without dropping the membrane enough to see those to connections. It could also be one or the other is loose on the top/fill end and is leaking there.