Ideally, an owner’s written consent to euthanasia exists and is kept as part of the medical record. If a "dropped off" animal’s owner didn’t leave you with a written consent of some sort, do not perform the procedure. (Have the animal declared abandoned and deliver it to a shelter instead. See the procedure at https://www.nysvms.org/resource/collection/E45CA734-8B73-4255-B861-5BED0FCBBAC9/abandonedanimals.pdf.) It is wise to be cautious about performing a euthanasia because the NYSED Office of Professional Discipline receives numerous complaints from animal owners about euthanasias performed on pets. Veterinarians have been disciplined for performing a euthanasia without consent of the owner, and also for improper administration of a euthanizing drug.
For euthanasia requests made in a pet owner’s will, it is true that animals are considered property and that an owner may request euthanization even if there
is no compelling medical reason to do so. Euthanasia is not considered animal cruelty, provided it is performed in accordance with the AVMA’s guidelines on humane euthanasia. However, a veterinarian who objects to a euthanasia request from an owner is not obligated to perform the euthanasia; in such
cases, the veterinarian is required to return the animal to the owner (or owner’s agent).
If the owner or agent will not take the animal back, you can have it declared abandoned if you don’t want to euthanize it. If you go through the abandoned animal procedure and eventually deliver the animal to a shelter, it can be put up for adoption or euthanized after 5 days.