It is legal for veterinarians to provide telemedicine services as long as they have established a Veterinarian-Client-Patient Relationship (VCPR).  If a VCPR is not established, veterinarians should refrain from diagnosing, prognosing or treating patients (with the exception of advice given in an emergency before the patient can be seen by a veterinarian, according to the AVMA's policy on telemedicine).  This question, as well as many others, is answered in the "Frequently Asked Questions" at https://www.avma.org/PracticeManagement/telehealth/Pages/telehealth-basics.aspx

The AVMA now has a resource page called Telehealth & Telemedicine in Veterinary Practice, which can be found at https://www.avma.org/practicemanagement/telehealth/pages/default.aspx.  Their intention is to help veterinarians provide services "with professionalism and adhering to the same standard of care, whether delivered in person or through electronic means." You can find links to telemedicine service models and case studies on the resource page, among other things.

The AVMA Practice Advisory Panel released a full report on telemedicine to the AVMA Board of Directors in January 2017.  You can see that report at https://www.avma.org/KB/Resources/Reports/Documents/Telemedicine-Report-2016.pdf.

If you haven't already read the article on telemedicine's key legal considerations in the September/October 2017 issue of Connections, you can find it here: http://www.nysvms.org/resource/collection/824a08a0-f7af-4d95-a850-c088f60c9c8e/NYSVMS-Sept-Oct_small.pdf?hhSearchTerms="telemedicine".