Imperfection sensitivity properties are investigated for an arch that has multiple member buckling at a limit point, which is classified as hilltop branching with multiple symmetric bifurcation points. The critical loads of imperfect structures are shown to be governed by a piecewise linear law of the imperfection parameter. Antioptimization problems are formulated to obtain the worst imperfection mode that most drastically reduces the critical load. A formula for the worst nodal imperfection as a linear combination of the critical modes is also presented. The validity of the formula is ensured by path-following analysis of arches with randomly generated imperfections.