I. No person shall file declaration of candidacy or primary petitions for nomination at the primary for incompatible offices. For the purposes of this section, incompatible offices shall include the offices of governor, United States senator, United States representative, representative to the general court, state senator, councilor, county commissioner, county sheriff, county attorney, county treasurer, register of deeds, and register of probate. If any person shall file for incompatible offices, the secretary of state shall advise the person of the provisions hereof and said person shall then advise the secretary of state which of said offices he or she wishes to retain in order to seek said nomination.
II. No person shall be nominated for incompatible offices. If a person shall be nominated for incompatible offices, the secretary of state shall advise the person of the provisions hereof and the person shall then advise the secretary of state which nomination the person wishes to retain; the secretary of state shall declare the nominations not retained by the person vacant.
III. A party shall not designate a person to fill a vacancy if the person has been nominated for any incompatible office.