Apparently, the answer is when you conceive the horse in Kentucky and it is born in New York, as happened with Funny Cide.

For those who care about horse bloodlines (and after today's third-place performance, I'm sure there are even fewer of us), it is some interest that Funny Cide's New York credentials come from the fact that he was born in New York as part of a marketing gimmick to allow the horse to run in state-only races.