The breakaway friction coefficient of curved surface sliders (CSSs) governs the transition between the sticking and the sliding behavior of the isolators, and hence affects the response of an isolated building during an earthquake. When the inertia forces induced by low-to-moderate intensity excitations are not able to overcome the breakaway frictional resistance of the CSS isolation system, the structure behaves as a fixed-base building, thus experiencing higher accelerations, interstorey drifts and internal forces than the isolated building. The majority of structural analysis programs disregard the static coefficient of friction, and implement the dynamic friction coefficient only throughout the response history analysis, which may imply an increased prediction of displacement demand for the isolation system but may lead to an unsafe design for the superstructure. In this paper, the frictional resistance to sliding before the breakaway is simulated through a bidirectional plasticity domain, which has been coded in a finite element of the isolator formulated in OpenSees to incorporate the transition between the breakaway friction in the sticking phase and the velocity-dependent friction model in the subsequent sliding phase. Based on this formulation, the influence of the breakaway friction on the response of buildings isolated with CSSs is investigated numerically through an extensive parametric study comprising more than 9000 bidirectional nonlinear time history analyses (NLTHAs). The parameters cover a range of friction coefficients, superstructure properties and a large group of natural spectrum-compatible bidirectional ground motions having different intensity levels and frequency contents. The results from NLTHAs are processed statistically to elaborate regression formulae and design recommendations that can be useful to predict the trigger acceleration at which sliding motion starts, as well as to suggest how to achieve more accurate estimates of the seismic response when the breakaway friction is ignored in the structural analysis model.