mtDNA is outside the nucleus of the cell and controls only the creation of the mitochondria (the part of the cell that makes electricity for the cell to survive). Sperm have no mtDNA but eggs do.
So all of us get this special form of DNA from our mothers and only our mothers. It does not mutate very often (unlike nuclear DNA) which is why it is not identifying. In anthropology, we use it to understand prehistory and human migration. My mtDNA is from Europe (H1) and we know that this particular version of mtDNA originated in Central Eurasia around 40,000 years ago (the original copy of our mtDNA is from Africa, 200,000 years ago).
Nowadays, there are about 30 majors groups of mtDNA and thousands of subgroups. So, it CAN be used in forensics - to exclude and include people. Nearly everyone has identical mtDNA to their own mother (99.999% of us do). And that's generally true for several generations back.
en.wikipedia.org
To use my own example, I should share H1 with all of my siblings, my mother, and all of her siblings, and my grandmother and all of her siblings from the same mom. Since it mutates so slowly, this would help identify me (if my body were unidentified) as far back as 5-10 generations. Some people's lines have had almost no mutations (llike mine - first there was H, then H1 - which appears around 28,000 years ago, so maybe 1 mutation in 12,000 years?)
Because of the way sexual reproduction/making of eggs and sperm works, nuclear DNA (except the Y chromosome) recombine and mutate and so...there are trillions of possibilities for what can make a new human, and with the exception of identical twins (in general), we are all unique in our nuclear DNA.
mtDNA can be very useful, though, in narrowing down a person to a percentage of the population that's less than 1%. In forensics, it's way more useful for figuring out the identity of human remains.
A hair (if the root is intact) would provide nuclear DNA - the DNA that identifies specific individuals. Skin cells (epithelial cells) do the same thing. mtDNA, though, can at least put us in the ballpark of identifying a person (esp. regarding heritage on the mother's side).
I am not caught up on this case, but it's my understanding that investigators have said they have found RH's wife's hairs, after taking a cheek swab. That means it's nuclear DNA, IMO. They couldn't possibly say it was her hair unless there was nuclear DNA.