Car-bike crash data from police reports show sidewalk cycling to be associated with the most common types of car-bike collisions in many urban and suburban areas. The most common cause of car-bike crashes in my city and some of the adjacent ones involves cyclists traveling contra-flow on the sidewalk, then being hit by right-turning drivers who aren't looking for contra-flow traffic.
It's hard to get accurate numbers to compare the number of miles of sidewalk cycling versus roadway cycling. In surveys of "avid" cyclists, the number of sidewalk miles is always tiny compared to the number of roadway miles. One commonly cited survey that measures crash frequency at different locations is here:
http://www.bicyclinglife.com/library/moritz2.htm
The vast majority of car-bike collisions occur at intersections, or involve cyclists crossing roadways, and sidewalk cycling complicates these maneuvers. Overtaking collisions are pretty rare, especially in urban areas where drivers are traveling more slowly and must pay more attention to avoid crashing into anything and everything from pedestrians to congested car traffic. As the frequency of intersections increases in denser areas, the safety benefits of riding on the roadway compared to the sidewalk become especially important.
Just make sure you use lights at night and follow the traffic rules.