The static electric polarizabilities (alpha) of a quadrupolar squaraine dye are investigated in silico, either as the excess polarizability, i.e., the change from the ground to the lowest excited state, Delta alpha, or as those of the two states separately, depending on the approach. The polarizabilities are worked out by making use of the energy and dipole moment Taylor expansions as a function of the electric field (E), in which alpha is represented by the quadratic and linear terms, respectively, and also by means of the linear response approach. Dipoles and energies are computed at a few values of the electric field, with different strategies that consider the geometry of the molecule either frozen in the ground state or relaxed at each E value. From a physical standpoint, the most appropriate approach to describing the molecular polarizability depends on the processes in which the molecule is involved: for example, fluorescence methods provide information about relaxed excited states, and absorption methods are used to determine the polarizability changes of excited states frozen in the ground-state conformation. We show that the excited-state polarizability does not strongly differ from the ground-state polarizability when the field is applied along the main axis of the squaraine. In contrast, remarkable differences are found when the field is applied perpendicular to the molecular plane due to a large geometrical distortion of the molecular backbone.