N.Y. Comp. Codes R. & Regs. tit. 9 § 4009.21
When a horse starts. Every horse shall be considered a starter when the stall gates open on the signal of the starter, unless the stewards declare a horse or horses non-starters because, in their opinion, the horses' chances were compromised leaving the starting gate. If so, all bets on the non-starters will be refunded unless the horse wins. For placing and program purposes, the non-starters will be considered to have run for purse only. If it be determined by the stewards that a horse is declared a non-starter, the money bet on the horse shall be refunded; if such horse is part of an entry or field, such circumstances shall be treated as a scratch for wagering as provided in section 4009.20 of this Part, notwithstanding the placing of any remaining part of the entry or field.
N.Y. Comp. Codes R. & Regs. Tit. 9 § 4009.21