N.Y. Comp. Codes R. & Regs. tit. 9, § 4024.1 – Registration required to enter or start.

(a) No horse may start in any race unless such horse is duly registered and named in the registry office of The Jockey Club, which is established for the identification of all horses whether foaled in the United States or in other countries and for the certification of their pedigrees. The entry of any such horse shall not be accepted unless such horses’s certificate of foal registration, certificate of foreign registration, or racing permit, whichever has been granted by The Jockey Club, is on file with the identification department of The Jockey Club.
1. (1) Tattoo requirement. No horse shall be allowed to enter or start in any race unless it has been tattooed in a manner satisfactory to the commission; except that the stewards may, in their discretion, allow a horse registered with the registry of a foreign country to start in a stake or invitational race upon such terms as they deem appropriate.
2. (2) No horse shall be allowed to enter or start unless a Jockey Club certificate of foal registration, certificate of foreign registration or racing permit is on file in the office of the racing secretary or other designated office of the track; except that the stewards may, in their discretion, for good cause, waive this requirement if the horse if otherwise properly identified.
(b)
(c) In addition, no horse shall be allowed to start unless the ownership of such horse has been duly registered in the Owners Registry of The Jockey Club established for recording the true ownership, including the proper names of all persons holding a proprietary interest, of all thoroughbred horses that race. The use of such data in the records maintained by the National Association of Racing Commissioners International, Inc., is hereby authorized.
(d) No horse shall be allowed to enter or start unless the certificate of foal registration, certificate of foreign registration, or racing permit, on file in the office of the racing secretary or other designated office of the track, has been endorsed by a State racing commission or commission, or a designated track official, or a Jockey Club certificate of ownership has been attached thereto, certifying to the registration of the horse in the Owners Registry of The Jockey Club.
(e) The stewards may, in their discretion, for good cause and for not over one race at a time, waive the requirements of subdivisions (c) and (d) of this section if the ownership is otherwise properly disclosed to their satisfaction.
(f) Upon transfer of any interest in a horse by sale, lease, claim or otherwise, it shall be the responsibility of the transferee managing owner to register such change in the Owners Registry with The Jockey Club and to cause the stewards at each track to be informed before that horse starts at such track.
(g) The commission, by order, may phase over a period of years, the requirement of registration in the Owners Registry, as set forth in subdivisions (c) and (d) of this section, by nature of transaction and age of horse.