There should never be a requirement for bicyclists to use the sidewalk. But it's allowed in many locations (whether it's desirable is another matter). Many cities and towns prohibit cycling on the sidewalk in business districts but allow it in the more outlying residential areas. Personally I avoid riding on the sidewalk except in rare circumstances where doing so for a short distance avoids a particularly hazardous road situation and only when there is either no or very limited pedestrian traffic. 'Bike Route' signs are an indication of streets that the city traffic department considers to be particularly well-suited to bicycling, but bicyclists are free to use other roads as well.