Legal Question in Traffic Law in California

Do you mean a line dividing the two directions of traffic? There is no requirement that such a line exist. The public entity is free to decide how it wishes to mark the street surface. If your question is really can you be found by the police to have been at fault for driving on the wrong side of the street when there is no center dividing line, sure, as it is clear whether you were on the wrong side of the street or over the middle of the street without there being a painted line. You did not get a ticket for being over a non-existant line, but for driving on the wrong part of the street.