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Here is the consular information sheet for Mexico:
---------------- quoted content from the Mexican Consul official site regarding animal importation
In order to bring a pet (dogs and cats) into Mexico, the following documents must be presented at the Office of Animal Health Inspection (OISA) at international airports and ports of entry into Mexico :
If the pet is less than tree months, a "Certificate of Good Health" issued by an official authority or by a licensed veterinarian provided that his or her signature is approved in the United Kingdom and issued not more than five days before the animal enters Mexico
If the pet is older than three moths, the "Certificate of Good Health" must also states immunizations against rabies, distemper, hepatitis and leptospirosis. Any immunization must been administered at least 15 days before pet's arrival to Mexico, but not more than one year.
At the OISA your pet will be physically checked and that office will determine if the animal is allowed immediate entry or must remain in custody for an additional inspection. In the first case, it will be issued a zoo-sanitary importation certificate, which must be carry when leaving Mexico. In the second case, If the above said authorities retain the animal, they should also give you a voucher.
If your pet is coming from a country where foot-and-month disease or risk of that disease exists, it must receive a prophylactic treatment.
They make no special provision for if the animal is a service animal. So for the purposes of travel, he must meet the pet requirements above.
To return to the US, you will need a current rabies certificate that lists the name of the rabies vaccine used, lot number, and date of injection. http://www.cdc.gov/animalimportation/dogs.html (requirements to return to the US)
Be aware that Mexico is not bound by the Air Carrier Access Act. They can require that your dog enter their country in cargo. Some countries do that. The airline will know if this is the case. Probably not, ie probably he can fly in cabin, but be prepared that this is a possibility.
You should contact the Consul office to learn about any laws regarding public access with service animals while in Mexico. Most countries do not recognize the range of service animals that the US does. Some recognize only guide dogs, and some none at all. I'm guessing that Mexico will be fairly similar to the US in this respect, but you can't count on it, so ask.