Each political subdivision required to make payments under §8-38-111 is authorized to impose upon each of its employees, as to services which are covered by an approved plan of agreement, a contribution with respect to the employee's wages, not exceeding the amount of the employee's tax which would be imposed by the “Rate of Tax” sections of the Federal Insurance Contributions Act (26 U.S.C. 3101 et seq.), if such services constituted employment within the meaning of that act. Each political subdivision is authorized to deduct the amount of such contribution from the employee's wages. Failure to deduct such contributions shall not relieve the employee or employer of liability for such contributions.