Police officers from the Bronx crossed into Manhattan and drove to the animal shelter on 110th Street with a dog in a cage. It wore no tag. Workers at the shelter passed a scanner across the scruff of his thick neck, looking for a microchip. Nothing.

They gave him a shot of vaccine and a checkup. This was no furry little lapdog. Part Am Staff — short for American Staffordshire terrier, one of the breeds that is sometimes referred to as a pit bull — the dog was upset, “unsure and uncomfortable,” said Julie Bank, executive director of Animal Care and Control of New York City, which runs the shelter and others.