In this paper, we study the cosymplectic statistical structures of constant ϕ-sectional curvature based on cosymplectic space forms. For higher than 3-dimensional cosymplectic space forms, we prove that the cosymplectic statistical structure of constant ϕ-sectional curvature on which must be unique and we determine it completely. For 3-dimensional cosymplectic space forms, we give an example to show that the cosymplectic statistical structures of constant ϕ-curvature are not unique, and we also obtain a rigidity theorem in this case.