The critical magnetic behavior of the colossal magnetocapacitive spinel CdCr₂S₄ is revisited. Magnetization and susceptibility of single-crystalline samples measured in the temperature range 68-120 K were analyzed by the kink-point method, the modified Arrott plots, the Kouvel-Fisher method, ln M versus ln H_eff, and the scaling analysis. We show that the critical exponents β = 0.365 and γ = 1.387 of the three-dimensional (3D) Heisenberg model describe the magnetic critical behavior only in the asymptotic region. Outside the asymptotic region, the values of β are reduced and those of γ are increased. We provide experimental evidence that the critical behavior of CdCr₂S₄ follows that expected for an ideal 3D Heisenberg system, however, in an unusual narrow window of temperature and in low magnetic fields only.