A person seeking to have the person's name printed on the ballot as a candidate for director must file with the board secretary a petition requesting that action. The petition must:
(1) be signed by at least 10 registered voters of the district, as determined by the most recent official list of registered voters, who:
(A) reside in the appropriate single-member district, if the person seeks to become a candidate to represent a single-member district; or
(B) reside anywhere in the district, if the person seeks to become a candidate to represent the district at large;
(2) be filed not later than the 31st day before the date of the election; and
(3) specify the single-member district the person seeks to represent or specify that the candidate seeks to represent the district at large.