N.Y. Comp. Codes R. & Regs. tit. 18, § 635.5 – Federal participation in payments for MA.

(a) Payments for medical care, services and supplies shall not be eligible for Federal participation if the recipient was not eligible for MA in the period during which care, services and supplies were received.
(b) The determination of eligibility for Federal participation in the cost of medical care, services and/or supplies rendered to recipients shall be made by the local social services districts prior to submission of any claim for reimbursement.
1. (1) Federal reimbursement for expenditures allocable to medical services provided by or in private child-caring institutions and agencies is available on the basis of a per capita, per diem rate established by the department, based upon medical cost reports submitted by such instructions and agencies.
2. (2) Federal reimbursement is also available for expenditures made by local social services districts to hospitals for hospital care provided to children placed in private nonmedical institutions or agencies.
(c)