LE will be the only people to get them at this point--maybe. This area was at one time my specialty.
When a person comes in with no ID, they are registered as a Jane or John Doe (or some other hospital specific code for unknown persons) until their identity is known. If it's not known then it remains under that code. Example, one time we had a lady come in to the ER who was acting very bizarre, erratic, kept stating that she didn't want to give her name because "they" could find her. She remained Female, 37 in the hospital's computer.
Finding the records would be easy enough, as all that would be needed would be the dates she would have been admitted to the hospital and checking the list for un-ID'ed patients.
At any rate, with HIPAA running around (even before then, but especially now) only the patient or the patient's authorized representative can get records. Lawyers can subpoena them with patient's consent. LE will need the same thing.
In this case...there MIGHT be a possibility of LE getting records without consent but it could be a fight. There's no relatives that we know of, patient cannot give consent, but as it's up to each facility to determine how to apply HIPAA, they might or might not have a fight to get the records.
This would need to be done relatively soon. I believe AZ law for hospitals is keeping the records onsite for 10 years from last date seen, then moved off-site and eventually destroyed. If it's not exactly this, it's something somewhat similar most likely.