As of December 16th, 2019, dogs and cats from the USA and Canada no longer need a health certificate to enter Mexico. Upon arrival they may be inspected by SENASICA, an acronym for the Mexican government's Servicio Nacional de Sanidad, Inocuidad, Calidad Agroalimentaria where the inspector will verify:
Your pets will NOT be placed in quarantine when entering Mexico, as long as they do not present signs of ectoparasites or ticks.
According to the CDC: Adult dogs older than 15 months of age that have previously received a rabies vaccination given no earlier than 3 months of age and that has since expired may be imported immediately following booster vaccination, without the need to wait for 30 days.
Dogs that have never received a rabies vaccination before must be vaccinated at least 30 days prior to arrival in the US.
Importation of dogs and cats into the US is regulated by the Center for Disease Control (CDC). According to the CDC, all domestic cats and dogs must show no evidence of disease that can be communicable to humans at the port of entry.
Even if all of your paperwork is in order, if your dog or cat does not look like it is in good health, further examination by a licensed vet (at your expense!) will be necessary before your dog or cat is allowed to re-enter the US!
Yes. Information can be found on the USDA Animal and Plant Health Inspection Service website.