The officers named in section 1 of this article shall be elected by the qualified electors of the state at the time and places of voting for members of the legislature, and the persons, respectively, having the highest number of votes for the office voted for shall be elected; but if two (2) or more shall have an equal and the highest number of votes for any one (1) of said offices, the two (2) houses of the legislature at its next regular session, shall forthwith, by joint ballot, elect one (1) of such persons for said office. The returns of election for the officers named in section 1 shall be made in such manner as may be prescribed by law, and all contested elections of the same, other than provided for in this section, shall be determined as may be prescribed by law.