The New Mexico Department of Homeland Security and Emergency Management is the agency tasked with disaster preparedness in the state (http://www.nmdhsem.org/). The 2013 Emergency Operations Plan can be obtained on its website at http://www.nmdhsem.org/Emergency_Operations_Plan.aspx.
The "All-Hazard Emergency Operations Plan" has a specific Emergency Support Function (ESF) dealing with animals. In the beginning of the document, each Emergency Support Function (ESF) is outlined. ESF #11 is entitled "Agriculture and Natural Resources" and states:
This ESF leads the response to emergencies or events involving commercial food supplies, nutrition assistance, animal disease outbreaks, plant pathogen or pest outbreaks, the need to protect natural and cultural resources and historic properties resources, and animal safety provisions.
One of the listed activities is to:
Provide for the safety and well-being of household pets, service animals, farm animals, and zoo animals during an emergency response or evacuation situation (page 63 of attached pdf).
ESF #11 is listed on page 211 of the attached pdf. Under the section on "Organization and Assignment of Responsibilities," the following is delegated to the State Veterinarian and his or her designees:
Provide for the safety and well-being of household pets and service animals during an emergency response or evacuation situation.