Residents should park on the even side of the road or remove their parked cars from the roadways completely so town work crews can clear the roads.
The parking ban will be in effect until noon Tuesday.
A Winter Weather Advisory is in effect for all Connecticut until midnight. The snow will turn to freezing rain by evening and to rain by early Tuesday, causing dangerous travel conditions, the National Weather Service warned.
Tuesday will be 50 degrees with heavy rain.
Click here to follow Daily Voice Stratford and receive free news updates.