The director of social services or his or her designated representative or the director of the county department of social services of the county where the custodial parent or minor child or children or child or children who have reached 18 years of age reside or the director’s designated representative may proceed in the same manner and under the same circumstances as provided in section 1 and 1a against the noncustodial parent for the support of the custodial parent and minor child or children or child or children who have reached 18 years of age if the custodial parent and minor child or children or child or children who have reached 18 years of age or any of them are being supported, in whole or in part, by public assistance under the social welfare act, Act No. 280 of the Public Acts of 1939, as amended, being section 400.1 to 400.121 of the Michigan Compiled Laws. The burden of proof shall be the same as provided in section 2.