Yes, chlorine evaporates out of water within 24 hours normally. It does depend on your volume of water If you had 100 gallons of cold water, some of the chlorine may stay in the water still. Agitation helps evaporate it from the water. Boiling or microwaving does this instantly.
This does not remove chloramines though. Not all city water uses this, so you would have to check with your water department, but as far as I know, using some sort of product to neutralize it is the only way to get rid of chloramines in the water.