Sec. 4. (a) At a primary election each political party subject to section 2 of this chapter shall nominate its candidates for the following offices to be voted for at the general election:
(1) United States Senator.
(2) Governor.
(3) United States Representative.
(4) Legislative offices.
(5) Local offices.
(b) In addition, each political party subject to section 2 of this chapter shall:
(1) vote on candidates for nomination as President of the United States;
(2) elect delegates from each county to the party's state convention; and
(3) elect a precinct committeeman for each precinct in the county if precinct committeemen are to be elected under section 4.5 of this chapter.