The district held the election Tuesday at Fire Station 1, and 105 people voted.
Woodman, an incumbent who ran unopposed for a two-year term on the board, received 91 votes. Branson took 72 votes, and Lucero drew 68. Incumbent Lori Johnson missed out on a board seat, earning 45 votes.
Lucero, current board president and Cortez city councilman, will serve a four-year term along with Branson.
The last Fire Protection District election was in 2014, in which 167 ballots were cast, said district administrator Wendy Mimiaga.
