My legal and medical knowledge is limited, but I believe only a MD can declare a person dead. Also, the location and time of the official declaration occasionally has a big effect on settling the person's estate. Hence the declaration is best made at the arrival gate where the local ME has jurisdiction.
I am more savvy on the aviation side of things and there is nothing in the FAR's that requires impounding the aircraft, unless an inflight death requires preservation of evidence for an accident or crime investigation (e.g. unbelted passenger in turbulence, passenger killed in onboard fight, etc)
RIP to the passenger and their family.