N.J. Stat. § 19:14-12
The county clerk shall draw lots in his county to determine which columns the political parties which made nominations at the next preceding primary election shall occupy on the ballot in the county. The name of the party first drawn shall occupy the first column at the left of the ballot, and the name of the party next drawn shall occupy the second column, and so forth.
The position which the names of candidates, and bracketed groups of names of candidates nominated by petitions for all offices, shall have upon the general election ballot, shall be determined by the county clerks in their respective counties.
The manner of drawing the lots shall be as follows: paper slips with the names of each political party written thereon, shall be placed in capsules of the same size, shape, color and substance and then placed in a covered box with an aperture in the top large enough to admit a man's hand and to allow the capsules to be drawn therefrom. The box shall be well shaken and turned over to thoroughly intermingle the capsules. The county clerk or his deputy shall at his office, draw from the box each capsule separately without knowledge on his part as to which capsule he is drawing.
The person making the drawing shall open the capsule and shall make public announcement at the drawing of each name, the order in which name is drawn and the office for which the drawing is made.
Where there is but one person to be elected to an office, the names of the several candidates who have filed petitions for such office shall be written upon paper slips and placed in separate capsules of the same size, shape, color and substance. The capsules shall be placed in a covered box with an aperture in the top large enough to admit a man's hand and to allow the capsules to be drawn therefrom. The box shall be turned and shaken thoroughly to mix the capsules and the capsules shall be withdrawn one at a time.
When there is more than one person to be elected to an office where petitions have designated that certain candidates shall be bracketed, the position of such bracketed names on the ballot (each bracketed group to be treated as a single name), together with individuals who have filed petitions for such office, shall be determined as above described.
Any legal voter of the county or municipality, as the case may be, shall have the privilege of witnessing the drawing.
The name or names of the candidate or bracketed group of candidates first drawn from the box shall be printed directly below the proper title of the office for which they were nominated, and the name or names of the candidate or bracketed group of candidates next drawn shall be printed next in order, and so on, until the last name or bracketed group of names shall be drawn from the box.
The arrangement of names of any bracketed group of candidates for any office for which more than one are to be elected shall be printed in the same order on the ballot as they were arranged on the petition of nomination.
The drawing for the positions which the names of candidates and bracketed groups of names of candidates, nominated by petition for office, and for the columns which the political parties which made nominations at the next preceding primary election and for the general election shall occupy upon the general election ballot, shall be held at 3 o'clock in the afternoon of the eighty-fifth day prior to the day of the general election.
N.J.S. § 19:14-12