The short answer is yes.
Here's the law on this: (42 CFR 447.30 )
The Federal share of Medicaid payments may be withheld from any provider specified in paragraph (c) of this section to recover Medicare overpayments that CMS has been unable to collect if the provider participates in Medicaid and—
(1) The provider has not made arrangements satisfactory to CMS to repay the Medicare overpayment; or
(2) CMS has been unable to collect information from the provider to determine the existence or amount of Medicare overpayment.
(c) The Federal share of Medicaid payments may be withheld with respect to the following providers:
(1) An institutional provider that has or previously had in effect a Medicare provider agreement under section 1866 of the Act; and
(2) A Medicaid provider who has previously accepted Medicare payment on the basis of an assignment under section 1842(b)(3)(B)(ii) of the Act; and during the 12 month period preceding the quarter in which the Federal share is to be withheld for a Medicare overpayment, submitted no claims under Medicare or submitted claims which total less than the amount of overpayment.
(d) Order to reduce State payment.
(1) CMS may, at its discretion, issue an order to the Medicaid agency of any State that is using the provider's services, to reduce its payment to the provider by the amount specified in paragraph (f) of this section.
(2) The order to reduce payment to the provider will remain in effect until—
(i) The Medicaid agency determines that the overpayment has been completely recovered; or
(ii) CMS terminates the order.
(3) CMS may withhold FFP from any State that does not comply with the order specified in paragraph (d)(1) of this section to reduce payment to the provider and claims FFP for the expenditure on its quarterly expenditure report.
(e) Notice of withholding.
(1) Before the Federal share of payments may be withheld under this section, CMS will notify the provider and the Medicaid agency of each State that CMS believes may use the overpaid provider's services under Medicaid.
(2) The notice will include the instruction to reduce State payments, as provided under paragraph (d) of this section.
(3) CMS will send the notice referred to in paragraph (e)(1) by certified mail, return receipt requested.