The state of Colorado or the county, as the case may be, at whose expense such child is kept shall be entitled to recover from the parent, legal guardian, or other person responsible for the support of such child such sum for the care, support, and maintenance of the child as may be reasonable therefor, and in no case shall such sum be less than the per capita monthly or yearly amount of expense in the institution in which the child is confined or the actual expense incurred by the state or county for the care and maintenance of such child. Any action or proceeding by the state or county against any parent shall be conducted in accordance with the procedure in civil cases. In case any action is maintained by the state, it shall be brought in the name of the people of the state of Colorado, and any moneys recovered in any action shall be paid to the state treasurer and credited to the particular fund for the benefit of the institution having the custody and care of such child. If an action is maintained by the county in cases where the county pays the expense of the care and maintenance of such child, such action shall be in the name of the board of county commissioners of such county or other body performing the functions of a board of county commissioners, and any amount collected in any such action shall be paid to the county treasurer of such county. When such action is prosecuted to a final judgment and judgment is rendered in favor of the people of the state of Colorado or the board of county commissioners of the county prosecuting such action, as the case may be, an execution may issue against the property of the defendant as in other civil cases.