The poodle-mix, named Nino, was given to the owner as a birthday present by her daughter in April 2000.
He went missing two years ago from the owner's yard, and when found Tuesday was suffering from bacterial infections, skin lesions, trauma and other injuries of unknown origin.
Video showed two women dropping the dog off outside the clinic on Main Street. Nino was discovered by an employee around 9 a.m.
The dog had an implanted identification chip, and the original owner was contacted.
"This beloved dog went missing from his owner and more than a year later was found discarded and in horrifying condition on a Hempstead street," Acting District Attorney Madeline Singas said. "Those who harm innocent animals, often hurt people, and we're seeking the public's help to find the criminal who stole and abused this innocent animal."
After Nino received stabilizing medical care, he was transferred to a private veterinary facility where he will be reunited with his owner.
The NCDA's Animal Crimes Unit is seeking assistance from the public in locating the persons responsible for Nino's condition and abandonment. The 24-hour tip line is 516-571-7755, option 8. Calls may be anonymous.