has the information you need starting at page 14.
Basically you need a death certificate, a Consular Mortuary Certificate, your affidavit and a transit permit. The Consular Affairs section of the Embassy should be able to assist you with this. Page 15 at the above link states:
(3) Affidavit by the Local Funeral Director. Attach to the consular mortuary certificate an affidavit or sworn declaration of the funeral director or person responsible for preparing the remains for shipment. This affidavit must state that the casket contains only the remains of the deceased and the necessary clothing and/or packing. When necessary to comply with any State regulations, the affidavit should also contain a statement that the body has been embalmed or otherwise prepared. If practicable, the affidavit should be executed before a consular officer
. When this is not practicable, it must be executed before a qualified local official whose signature can be authenticated by a consular officer.http://kingston.usembassy.gov/reporting_death_abroad.html
"The U.S. Embassy will need the following documents to process the Consular Report of Death:
Certified Jamaican death certificate
Proof of U.S. CitizenshipReport of Death worksheet
(PDF 53 kb)
In sudden or accidental deaths, Jamaica requires a post-mortem exam be done and a coroner’s inquest be held before a death certificate can be issued. As a result, it can take several months for the Jamaican authorities to issue a death certificate. To facilitate the settling estate matters, the U.S. Embassy may issue a Preliminary Report of Death Abroad based on the autopsy report."
I hope this information is helpful.