I'm not in medicine, but I am in insurance.
Based on new privacy laws that went into effect on April 15 of this year, finding out directly from the hospital would be nearly impossible. You'd basically need the express written consent (not of major league baseball) of the deceased/donor or next-of-kin. That's pretty hard to get when you don't know who they are.
You'd have to be indrect, checking news stories and such, as suggested earlier or breaking in.
I don't know if there's been precedent on this or not, but I'm not sure how anxious a judge would even be to allow a subpoena (sp?) or search warrant for the records. Even then, since HIPAA is the governing law, it might have to be a federal judge that issued the order. But then, that kinda goes against the clandestine nature of Dark*Matter.