N.Y. Comp. Codes R. & Regs. tit. 9, § 4108.9 – General procedure.

(a) For all overnight races other than invitational races the starters shall be determined by lot from those properly declared in with preference. The names of all horses declared shall be posted by race with preference dates. However, where necessary to fill a card, one conditioned race per day may be divided into two divisions and the divisions may be selected by the racing secretary.
(b) For all races other than handicap races the post positions of all starters and also eligibles shall be drawn by lot.
(c) A substitute race may be provided for each day's program and shall be so designated. The substitute race shall be used only if regularly scheduled races fail to fill and if a regularly scheduled race is not divided. No substitute or other race may be used as part of the next program.
(d) A fair and reasonable racing opportunity shall be afforded all horses and conditions shall not be written in such a way that any horse is deprived of a fair opportunity to race.
(e) The name of each horse at the track ready to race shall be posted by gait in the declaration room together with all pertinent information concerning such horse which may be required to determine eligibility of such horse to races at the track. The names of horses invited to invitational races shall be posted at least 18 hours prior to the close of declarations.
1. (1) Handicap races are permitted where provided for in the published condition book and in conformity with such conditions with post positions determined according to the relative standings within such conditions (including claiming prices). No time records or bars shall be used as a condition.
2. (2) Handicap races are permitted for preferred races or for invitational races. In such races all post positions may be assigned by the racing secretary if the horses are invited and the names of the invited horses and their post positions are posted in the declaration room at least 18 hours prior to closing of declarations thereto.
(f)
(g) In an overnight race the racing secretary, with the approval of the presiding judge, may reject the declaration of any horse which has a past performance indicating that it is below the competitive level of the other horses declared providing such rejection does not result in cancellation of the race.