In counties, cities, school districts and other municipalities, or part thereof, where registration of voters is required in the entire territory thereof, the signatures to petitions which assert that the petitioners are “legally qualified electors” or words of like effect in conformity with the applicable statute shall be accepted, by the officer determining the sufficiency of petition signatures, as proper signatures, so long as persons of the same names or ones of such similarity as to reasonably appear to be the same persons are contained in the registration books, and so long as the address of the petitioner is furnished, unless such official has reasonable evidence that the asserted signature in question is not in fact the signature of the person it purports to be, or that the signature though genuine is not the signature of a duly qualified elector. The secretary of state shall adopt rules and regulations for the guidance of county election officers and other officers as specified by law in making determination under this section of sufficient similarity of names on petitions and names in registration books.