Does your dog really belong in this restaurant?

NEW YORK - On a quiet weekday evening inside a restaurant in Brooklyn, a dog under a table announced its presence with a single pronounced yap. At a scoop shop in downtown Manhattan, a large white poodle was spoon-fed what appeared to be vanilla ice cream. In the dining room of a chic Midtown restaurant, a teacup Pomeranian strutted across the floor.

When it comes to dogs in restaurants, two things can be true at once: first, according to the New York City health code, "no live animal shall be kept, housed or permitted to enter into or remain in any food service establishment," with a few exceptions, including service animals and city-approved dog cafes such as Boris & Horton.

Second: the dog nibbling a french fry at the next table.

There are 617,000 licensed dogs in New York City, and the vast majority, presumably, eat in. But while no city agency tracks how...