Should a county find that it is impossible to pay the amounts required under this chapter or RSA 161, it may file a petition with the commissioner of the department of health and human services requesting financial aid. The commissioner of health and human services shall cause an investigation to be made of all pertinent factors relating to the financial circumstances of the petitioning county. The commissioner of health and human services may, with the approval of the governor and council, loan or grant to such county such amount as may be necessary.