Is there any internal connection between the eyes and the mouth maybe a passage through which a liquid put in the eye can reach the mouth?

Yes, there is an internal connection between the eyes and the mouth via the nasolacrimal duct. Tears produced in the lacrimal glands drain through this duct into the nasal cavity, which is connected to the throat and mouth. Thus, if a liquid were to enter the eye, it could potentially travel through this pathway to reach the mouth. However, this is not a direct passage for liquids and is not intended for that purpose.