They can't make it there, apparently, thanks to guildlike professional licensing laws. Details from the UK Guardian:
Women can not legally give birth at home in the presence of a trained and experienced midwife.
This city of more than 8 million people, with its reputation for being at the cutting-edge of modern urban living, now lacks a single midwife legally permitted to help women have a baby in their own homes. "It's pretty shocking that in a city where you can get anything any hour of the day a person cannot give birth at home with a trained practitioner," said Elan McAllister, president of the New York-based Choices in Childbirth.
The collapse of New York's legal home birth midwifery services has come as a result of the closure two weeks ago of one of the most progressive hospitals in the city, St Vincent's in Manhattan. When the bankrupt hospital shut its doors on 30 April the midwives suddenly found themselves without any backing or support.
There are 13 midwives who practise home births in New York, and under a system introduced in 1992 they are all obliged under state law to be approved by a hospital or obstetrician, on top of their professional training.
St Vincent's was prepared to underwrite their services, but most other doctors and institutions are not, and they now find themselves without the paperwork they need to work lawfully.
Wondering if you can legally hire someone to help you give birth if you want? Check this useful state-by-state chart of the arcane arts' legal status.