From the NYC Taxi and Limousine Commission website.  http://www.nyc.gov/html/tlc/html/faq/faq_pass.shtml

"Drivers of yellow medallion taxicabs and for-hire vehicles and their passengers, are exempt from laws regarding car seats and seatbelts.  Keep in mind, the TLC encourages everyone in the vehicle to buckle their seatbelts while riding in a cab.  There are no Taxi and Limousine Commission rules regarding this, as it is a State exemption. Passengers with children are encouraged to bring their own car seats, which the drivers must allow passengers to install. *NOTE - Children under the age of seven are permitted to sit on an adult's lap."