Context. Measurable linear scattering polarization signals have been predicted and detected at the solar disk center in the cores of chromospheric lines. These forward-scattering polarization signals, which are of high interest for magnetic field diagnostics, have always been modeled either under the assumption of complete frequency redistribution (CRD), or taking partial frequency redistribution (PRD) effects into account under the angle-averaged (AA) approximation. Aims. The aim of this work is to assess the suitability of the CRD and PRD–AA approximations for modeling the forward-scattering polarization signals produced by the presence of an inclined magnetic field, the so-called forward-scattering Hanle effect, in the chromospheric Ca I 4227 Å line. Methods. We performed radiative transfer calculations for polarized radiation in semi-empirical 1D solar atmospheres out of local thermodynamic equilibrium. We applied a two-step solution strategy. We first solved the problem considering a multilevel atom and neglecting polarization phenomena. Subsequently, we solved the same problem, this time considering a two-level atom and including polarization and magnetic fields. By keeping the population of the lower level calculated in the previous step fixed, the problem of step two is linear and is solved with a preconditioned FGMRES iterative method. We analyzed the emergent fractional linear polarization signals calculated under the CRD and PRD–AA approximations and compared them to those obtained by modeling PRD effects in their general angle-dependent (AD) formulation. Result. With respect to the PRD–AD case, the CRD and PRD–AA calculations significantly underestimate the amplitude of the line-center polarization signals produced by the forward-scattering Hanle effect. Conclusions. The results of this work suggest that a PRD–AD modeling is required in order to develop reliable diagnostic techniques exploiting the forward-scattering polarization signals observed in the Ca I 4227 Å line. These results need to be confirmed by full 3D calculations including non-magnetic symmetry-breaking effects.