2016 New York Laws
PML - Racing, Pari-Mutuel Wagering and Breeding Law
Article 2 - (Racing, Pari-Mutuel Wagering and Breeding Law) THOROUGHBRED RACING AND BREEDING
225 - Registration of race horses.

  225.  Registration  of race horses. The true name, sex and age, and
  also the pedigree, unless such pedigree  is  unknown,  of  every  horse,
  mare,  gelding,  colt or filly shall be registered with the jockey club,
  United States trotting association, American quarter  horse  association
  the  national  steeplechase and hunt association or such other entity as
  the racing and wagering board may designate before it shall be  eligible
  to  compete  in  any  race conducted under a license or franchise of the
  state racing and wagering board and such name shall continue to  be  its
  true  name  unless  and until the same shall be changed according to the
  rules and regulations of such organization. The class to which any  such
  animal  belongs  for the purpose of the entry or competition in any race
  shall be determined by the public performance thereof in former contests
  or trials of speed, as prescribed by the printed rules  of  the  person,
  association or corporation sponsoring such race.