WAs the dresser stored in a damp area or in a colsed in space? If yes then the dresser has probalby absorbed some moisture and it may have some mildew or mold growing on it or in it.
I would first place it in a dry sunny room, washing it gently with mild soap and water, using only a damp sponge.
If you can see the mildew growing you are going to have to kill it. You can do this with a solution of 1 tablspoon household bleach to a gallon of water songed onto the offending mold/mildew. Try this in an inconspicuous spot first to see if it will damage the finish. RInse the bleach off after about fifteen minutes. It is really important to get rid of all of the mold or mildew or it will come back. I know this from experinece on my boat.
IF the dresser is not a valuable antique, you might go so far as to refinish it if the above does not work. If it is valuable or you are not sure then have a professional look at it. Nothing ruins the vlaue of a fine antique like redoing the finish on it.