A coyote killed a small dog on Smith Ridge Road following a scuffle Monday night, police said. Police on Tuesday responded to a report from a man who found the mauled body of a Yorkshire terrier on his property, officials said. While police investigated, the deceased dog’s owner could be seen searching for the animal and told authorities that she had been searching all night, according to Officer Allyson Halm, head of the New Canaan Police Department’s Animal Control section. Then on Wednesday, Halm said she received a report that a coyote was seen chasing two Cairn terriers on a Carter Street property. Fortunately, the dogs’ owner in that case stepped out and broke up the chase, she said.