N.Y. Comp. Codes R. & Regs. tit. 9, § 4109.5
If the claimant of a horse has requested post-race testing, at the expense of the claimant, on the claim form, then the judges shall designate such horse for post-race testing pursuant to section 4120.8(b) of this Title. The original trainer shall remain responsible for the claimed horse until any on-track post-race sample collection has been completed.