In this work we have used extensive Monte Carlo simulations and finite size scaling theory to study the phase transition in the dipolar planar rotator model (dPRM), also known as dipolar XY model. The true long-range character of the dipolar interactions was taken into account by using the Ewald summation technique. Our results for the critical exponents do not fit those from known universality classes. We observed that the specific heat is apparently non-divergent and the critical exponents are ν = 1.277(2), β = 0.2065(4) and γ = 2.218(5). The critical temperature was found to be T(c) = 1.201(1). Our results are clearly distinct from those of a recent renormalization group study from Maier and Schwabl (2004 Phys. Rev. B 70 134430) and agrees with the results from a previous study of the anisotropic Heisenberg model with dipolar interactions in a bilayer system using a cut-off in the dipolar interactions (Mól and Costa 2009 Phys. Rev. B 79 054404).