If the mental health board finds that a person committed to a state hospital for the mentally ill by the board has, or probably has, a legal settlement in some other county in the state, the board shall immediately notify the mental health board of that county of its finding and commitment. The board members so notified shall thereupon inquire and ascertain, if possible, whether the patient has a legal settlement in their county and shall immediately notify the chief executive officer of the hospital and the board members of the county from which the patient was committed of the result of their inquiry. If the legal settlement of a patient cannot for a time be ascertained and is afterwards found, the notices provided for in this section shall then be given.