Demolition of the elementary school began Tuesday.
A twister six blocks wide did an estimated $70 million damage to Chapman, population about 1,400.
Crystal Bishop, 21, was killed in the storm.
Despite getting millions in insurance, donations and government help, Chapman school officials say they will need a bond issue to repair school buildings damaged by the tornado.
The district needs to rebuild its elementary and middle schools, the district office, art building and three-fourths of its high school.
Last month, Chapman superintendent, Tony Frieze, said the school district will put a bond issue before voters in April.
Cost estimates aren't available, but Frieze estimated that the district would need $10 million or less for its share of the repairs.