Our friends at Phrase Finder have this to say:
"A ringer is a horse substituted for another of similar appearance in order to defraud the bookies. This word originated in the US horse-racing fraternity at the end of the 19th century. The word is defined for us in a copy of the Manitoba Free Press from October 1882:
"A horse that is taken through the country and trotted under a false name and pedigree is called a 'ringer.'"
Further,
"...So, that's ringer; what about dead? Dead, in the sense of lifeless, is so commonly used that we tend to ignore its other meanings. The meaning that's relevant here is exact or precise. This is demonstrated in many phrases; 'dead shot', 'dead centre', 'dead heat', etc.
So, 'dead ringer' is literally the same as 'exact duplicate'. It first came into use soon after the word ringer itself, in the US at the end of the 19th century. The earliest reference I can find that confirms the 'exact duplicate' meaning is from the Oshkosh Weekly Times, June 1888, in a court report of a man charged with being 'very (or dead drunk': ..."