True fossils will not contain any DNA that can be sequenced. Ancient bones that are not fossilized often have DNA fragments that are long enough to sequence, especially with the newer "next generation" sequencing technologies. There are a few genes in the nucleus of mammals (and humans are mammals) which are copies of mitochondrial genes. These are known as "numts". But other than these few sequences, all others can be recognized as either nuclear or mitochondrial based on their similarity to nuclear and mitochondrial sequences in modern day living humans (from which it is easy to separate mitochondria or nuclear genomic DNA for sequencing).
or a similar tool to look for similar sequences in a database (GenBank, or perhaps a database of just human nuclear and mitochondrial genomes), you can see whether it is part of the human nuclear genome, the mitochondrial genome, or contaminating DNA from some bacteria or fungus that infiltrated the bone before or after the human died.
Recently, plague bacteria from bones of victims who died of plague hundreds of years ago was sequenced. http://www.sciencedaily.com/releases/2013/05/130510075449.htm
Obviously you are trying to distinguish between sequences from the mtDNA and mt sequences migrated into the cell nucleus, usually known as NUMT. Alignment of the two sequences will show differences like much less nucleotide substitutions in the NUMT than in the mt DNA, (C+G) > (A+T) in the former and (A+T) > (C+G) in the mitochondria. We experienced a similar problem in the mammal species of guanaco so I suggest you to go to the publication:”The complete mitochondrial DNA sequence of the guanaco (Lama guanicoe): comparative analysis with The vicuna (Vicugna vicugna) genome”, there you will find some other clues to help you to solve your question.
The human, Neanderthal, chimpanzee and gorilla genomes have been sequenced. I don't think the chimpanzee ever got completely assembled, but it is fairly well finished.
There are several numts differences between human and chimpanzee published:
A comparative analysis of numt evolution in human and chimpanzee.
Hazkani-Covo E, Graur D.
Mol Biol Evol. 2007 Jan;24(1):13-8. Epub 2006 Oct 20.
PMID: 17056643
A comparative approach shows differences in patterns of numt insertion during hominoid evolution.
Jensen-Seaman MI, Wildschutte JH, Soto-Calderón ID, Anthony NM.