A special meeting of the county board of commissioners of a county shall be held only when requested by at least 1/3 of the members of the county board of commissioners of the county. The request shall be in writing, shall be addressed to the county clerk, and shall specify the time, date, place, and purpose of the meeting. Upon the reception of a request, the clerk shall give notice to each of the commissioners in the manner required by the bylaws or rules of the county board of commissioners or, if the bylaws or rules do not specify the manner for giving notice to each of the commissioners, by causing notice to be delivered to the commissioners personally, or by leaving the notice at the residence of the commissioner, or by mailing a copy of the notice to his or her post office address by certified mail with return receipt requested, at least 10 days before the time of the meeting. Public notice of the time, date, and place of the meeting shall be given in the manner required by the open meetings act, Act No. 267 of the Public Acts of 1976, being sections 15.261 to 15.275 of the Michigan Compiled Laws.