If the employer is a State or political subdivision thereof, or an agency or instrumentality of any one or more of the foregoing, the return of the amount deducted and withheld upon any wages under section 3101 and the amount of the tax imposed by section 3111 may be made by any officer or employee of such State or political subdivision or such agency or instrumentality, as the case may be, having control of the payment of such wages, or appropriately designated for that purpose.
26 U.S. Code § 3126. Return and payment by governmental employer
Section, except as otherwise provided, effective with respect to payments due with respect to wages paid after Dec. 31, 1986, including wages paid after such date by a State (or political subdivision thereof) that modified its agreement pursuant to section 418(e)(2) of Title 42, The Public Health and Welfare, see section 9002(d) of Pub. L. 99–509, set out as an Effective Date of 1986 Amendment note under section 418 of Title 42.