This document below was received from USDA / USF&WS in the USA and is most probably the most important part of documentation on this site:
Rules to Follow on Importing Trophies (USA)
All hunters must be identified by their full given name, as it appears on their passport, which hopefully is the same as their birth certificate and social security card, on all documents; period!
Copy of the Hunt Register or Hunt Permit is REQUIRED to submit with every entry.
Only one hunter to a House Bill and crate/package.
The following is a list of animals that have special requirements being imported into the US:
Dip and Pack Shipments:
All Swine require shipment to a USDA Approved Establishment for further processing - Pack separately;
All Non-Human Primates require same as above;
All Non-Human Primates (Monkeys and Baboons) and Porcupines will require a CDC Permit as from 1 October 2012.
NO Ostrich (or ANY part of it) be be imported without the necessary VS-16-6 Import Permit.
Following rules on every shipment of dip and pack ruminants for inspection by CBP/Agricultural Specialist.
Clean, dry bones, horns, and hoofs, that are free from undried pieces of hide, flesh, and sinew and are offered for entry as trophies or for consignment to museums may be imported without other restrictions.
Hides or skins may be imported without other restriction, if found upon inspection, or by certificate of the shipper or importer satisfactory to said inspector, to be hard dried hides or skins.
Special Veterinary Permits for the following animals are required that must indicate what chemical process was used to render the animal non-infectious. Requires clearance by U.S. Department of Public Health before it can go to Fish and Wildlife for clearance.
All Dip and Pack shipments sent to Portland, Oregon - pilot project by FWS
All non-human primates (Monkeys and Baboons)
Following Animals may not be imported into the U.S. under any circumstances:
African Wild Dog
Scimitar Horned Oryx - Would have to have been ranch captive bred and taken prior to 09-02-2005, requires US CITES I permit.
Mountain Cape Zebra
Black Faced Impala
Also any animal at this website https://edecs.fws.gov/FilerSpeciesSearch.cfm?SEARCH=True which has a Red E in the ESA column. Means they are endangered and protected by the Endangered Species Act. It also applies for any animal with a Red Y in the MMPA column. Means the Marine Mammal Protection Act protects them.
Following rules on CITES Animals
All CITES Shipments now are required to have block 14 of the Export CITES permit completed with export endorsement after May 1, 2008 or the CITES animals will either be refused entry and re-exported back to origin at shippers expense or destroyed.
CITES I and II animals only permitted entry into U.S. if the animals were sport hunted by the actual importer of record. No shipments permitted entry if acquisition was in commercial trade and animal is listed as Threatened (Red T) in the ESA column.
All CITES I animals require a U.S. Import Permit and copy should be requested by the overseas agent before they start the export documentation process.
(In the U.S. Bontebok is considered a CITES I animal)
CITES III animals must be listed on a CITES Export Permit.
Birds - make sure they don't require Migratory Bird Permits.
Check the website https://edecs.fws.gov/FilerSpeciesSearch.cfm?SEARCH=True for any animal you may have questions on.