Any court or any family support magistrate having jurisdiction to make an order for support of any person by a legally liable relative or putative father shall have authority to direct payment in accordance with such order to the Commissioner of Administrative Services or to the welfare department of any political subdivision of the state for such period as such person shall receive welfare assistance from the state or such subdivision; and such court or family support magistrate, upon its findings of any arrearage due under any support order, shall have authority to determine that portion of such arrearage the failure to pay which resulted in grants of welfare assistance, and to order payment of such portion to the Commissioner of Administrative Services or the local welfare department which granted such assistance in reimbursement therefor, as the case may be. The provisions of this section shall apply to orders made under the provisions of sections 46b-60 and 46b-81 to 46b-87, inclusive, and 53-304.