A petition sheet shall contain only the signatures of qualified and registered electors of the city or township listed in its heading. For recall of a village officer the petition shall be signed by qualified and registered electors of the village. A qualified and registered elector may sign the petition sheet in any location at which the petition sheet is available. A petition is not invalid if it contains the signature of a person who is not a qualified and registered elector of the appropriate city, township, or village listed in the heading of that petition sheet.