I don't know about a legal responsibility, that would vary by state, but it's polite to not take an action that a neighbor informs you has caused damage to their property in the past. Could you use a hose to direct the water all the way to the street?
Will the little voice in the back of my mind screaming "This is a bad idea" please yield the floor. --Mikey
Chivalry be hanged, and so will you.