It is illegal (see the city's publication at below).
http://www.cityofnewhaven.com/streetsmarts/pdfs/smart_cycling_new_haven_handbook_1.pdf
That said, it is understandable that one might feel safer riding on the sidewalk. The problem arises when inconsiderate people do not have the courtesy or common sense to navigate slowly and carefully around pedestrians. Too many of the cyclists around the Yale area are selfish and careless.