Yes it is legal to ride your bike on the sidewalk as long as you are safe according to the Department of Transportation: http://www.ct.gov/dot/cwp/view.asp?a=3531&q=259440
They suggest walking your bike if you are on the sidewalk if there are pedestrians on the sidewalk with you but having a bell or someway to alert people that you are coming up near them so the rider or the walker aren't hurt by your vehicle is okay too.
It is not legal to ride your bike on the sidewalk in some places, like West Hartford center or New Haven. That's because local ordinances may restrict it.
Generally, it's unsafe to ride on sidewalks because cars in driveways won't see you as well and you can hit pedestrians.