All primary elections held by any political party in this state for the nomination of any state, national, district, circuit, county, or municipal officer shall be held and conducted under the provisions of this chapter and, except as herein modified, shall be held and conducted in the same manner and form, under the same requirements and subject to the same forfeitures, penalties, and punishments as are now or shall hereafter be provided by law for the holding of regular state elections, but nothing herein contained shall make it obligatory upon any political party or parties to hold a primary election.