Legally, the "MTA NEW YORK CITY TRANSIT AUTHORITY (NYCTA)" is neither a state or local government entity 

On March 1, 1968, the NYCTA, and its subsidiary, the Manhattan and Bronx Surface Transit Operating Authority (MaBSTOA), were placed under the control of, and are now affiliates of the Metropolitan Transportation Authority (MTA).

The Metropolitan Transportation Authority (MTA) is a public benefit corporation. New York state public benefit corporations and authorities operate like quasi-private corporations, with boards of directors appointed by elected officials, overseeing both publicly operated and privately operated systems. Public authorities share characteristics with government agencies, but they are exempt from many state and local regulations.

I am retired from the LIRR/MTA and living in NC.  I was hired in 1977.  Is my pension exempt under the Baileys law.

If your pension is vested in a state outside North Carolina, then you are not exempt under the Bailey's law.