Yeah, as Scott said you have to find out exactly what documentation you need to bring a parrot into China from the Chinese government/Embassy/Consulate, or whomever the governing-body in China is over importing animals/birds into the country. That's the only place you can find out exactly what you will need to have at Customs with your CAG and be able to trust the information you're given, and you need to do it ASAP, long before you are planning on leaving, because the requirements are completely different from country to country, some are extremely easy and only require a Certificate of Health signed by a Certified Avian Vet and then documentation of Proof of Ownership of the bird (usually a Bill of Sale from your bird's breeder or the paperwork/receipt from the pet shop, the original Hatch-Certifificate with the breeder's name and signature along with your bird's hatch-date and your signature on it, etc.; most-all countries are going to require these to documents, #1) Certificate of Health signed by a Certified Avian Vet, and #2) Proof of Ownership of your bird, and a lot of the time they'll also want the bird's original Proof of Age/Hatch-Certificate as well)...But as far as what each country will take as documentation of these 2 or 3 things, and then any other documentation/paperwork they want in-addition to these common requirements is just up to each, individual country, and you can only find that information out by calling the correct governing-body/agency in China...
***Have you spoken to anyone in the "Customs" department of China? That's a good place to start, either with Chinese Customs or as Scott said start by calling the US Embassy in China, which I believe is in Hong Kong, tell them you're moving from the US to China, you're wanting to bring your pet Congo African Grey with you into China and keep him as your pet while you're living there (make sure they know exactly what species of parrot you have), and ask them what person/people or agency you need to contact in-order to get a list of ALL the documentation/requirements that you'll need in-order to be able to bring your CAG into the country with you...And once you get each and every requirement you write them down in-detail, and then check them off as you go...Some are quick and easy, some countries are a royal pain in the butt...
***And on that note, you also need to find out if there is going to be a mandatory "Quarantine Period" and "Quarantine Station" where your CAG has to stay for a certain period of time before being released to you in China...For a lot of countries the Certificate of Health signed by an Avian Vet is all you need, probably for most countries that's all you need...However, there are countries where they have a mandatory Quarantine Period where your pet has to stay in a government-owned Quarantine facility for a certain period of time, and which you have to pay for his stay at before they'll release him to you, so you have to be ready for that (FIND OUT EXACTLY WHAT THE CERTIFICATE OF HEALTH NEEDS TO SAY!!! Like it may need to say that your CAG is free of certain, specific Avian Diseases or other specific requirements that your CAV will have to write-out correctly)...Then there are some countries that don't allow ANY animals to come into the country at all, like Australia/New Zealand, or they allow only certain species of Animals, Birds, Reptiles, etc. into the country...So you have to be very specific with information about your CAG and ask every little question and get every little detail about what you're going to need to have with you when you get off of the plane with your CAG...
I know we have a lot of members here who have moved from the US to Asian Countries with their Parrots, I don't know about China, but hopefully someone will be along who knows exactly who you need to contact in China to get all of the requirements/documentation you need...