Customs Border Protection (CBP) and Center for Disease Control (CDC) provide oversight of dogs and cats from international flights. There is a concern over the documentation of some of these animals and concern for their welfare. In many cases these animals have incomplete documentation. If documentation is not received then these animals will be returned to the country of origin at the expense of the airlines.
The Port Authority has recently issued a directive that states that handlers must provide safe and humane temporary holding facilities for these animals as their cased are reviewed and the disposition of legal entry is resolved.
The CBP has issued a Pipeline regarding the proper documentation and standards to be met for legal entry of these animals both from air cargo and passenger flights.
The ARK at JFK has proper facilities for these animals during this process and currently works with airlines to provide temporary facilities.
Here is a link to the CDC site for proper documentation.