The state agency, with the approval of the Governor, is hereby authorized to enter, on behalf of the State of Nebraska, into an agreement with the Secretary of Health and Human Services, consistent with the terms and provisions of sections 68-601 to 68-631, for the purpose of extending the benefits of the federal old age and survivors' insurance system to employees of the state or any political subdivision thereof with respect to services specified in such agreement which constitute employment. The state agency, with the approval of the Governor, is further authorized to enter, on behalf of the State of Nebraska, into such modifications and amendments to such agreement with the Secretary of Health and Human Services as shall be consistent with the terms and provisions of sections 68-601 to 68-631 if such modification or amendment is necessary or desirable to secure the benefits and exemptions allowable to the State of Nebraska or any political subdivision thereof or to any employee of the State of Nebraska or any political subdivision thereof provided by the Social Security Act, the Federal Insurance Contributions Act, or the employee tax. Such agreement may contain such provisions relating to coverage, benefits, contributions, effective date, modification and termination of the agreement, administration, and other appropriate provisions as the state agency and Secretary of Health and Human Services shall agree upon, but, except as may be otherwise required by or under the Social Security Act as to the services to be covered, such agreement shall provide in effect that:

(1) Benefits will be provided for employees whose services are covered by the agreement and their dependents and survivors on the same basis as though such services constituted employment within the meaning of Title II of the Social Security Act;

(2) The state will pay to the Secretary of the Treasury of the United States, at such time or times as may be prescribed under the Social Security Act, contributions with respect to wages equal to the sum of the taxes which would be imposed by the Federal Insurance Contributions Act if the services covered by the agreement constituted employment within the meaning of the Federal Insurance Contributions Act;

(3) Such agreement shall be effective with respect to services in employment covered by the agreement performed after a date specified in the agreement, but in no event may it be effective with respect to any such services performed prior to the first day of the calendar year in which such agreement is entered into or in which the modification of the agreement making it applicable to such services is entered into, except that if a political subdivision made reports and payments for social security coverage of its employees to the Internal Revenue Service under the Federal Insurance Contributions Act in the mistaken belief that such action provided coverage for the employees, such agreement shall be effective as of the first day of the first calendar quarter for which such reports were erroneously filed;

(4) All services which constitute employment and are performed in the employ of the state by employees of the state shall be covered by the agreement;

(5) All services which constitute employment, are performed in the employ of a political subdivision of the state, and are covered by a plan which is in conformity with the terms of the agreement and has been approved by the state agency under sections 68-608 to 68-611 shall be covered by the agreement;

(6) As modified, the agreement shall include all services described in either subdivision (4) or (5) of this section or both of such subdivisions and performed by individuals to whom section 218(c)(3)(c) of the Social Security Act is applicable and shall provide that the service of any such individual shall continue to be covered by the agreement in case he or she thereafter becomes eligible to be a member of a retirement system; and

(7) As modified, the agreement shall include all services described in either subdivision (4) or (5) of this section or both of such subdivisions and performed by individuals in positions covered by a retirement system with respect to which the Governor has issued a certificate to the Secretary of Health and Human Services pursuant to subsection (2) of section 68-624.