A Fano resonance, as often observed in scattering, absorption, or transmission experiments, arises from quantum interference between a discrete optical transition and a continuous background. Here, we present a temperature-dependent study on Fano resonances observed in photoluminescence from flakes of the layered semiconductor antiferromagnet chromium thiophosphate (CrPS4). Two Fano resonances with a distinctly different temperature dependence were identified. The continuous background that is responsible for the Fano resonances is attributed to the d-d transition of the optically active Cr3+ center, predominantly the spin-forbidden 2Eg → 4A2g transition with contributions of the broad-band 4T2g → 4A2g transition. The discrete states that interfere with this continuous background are suggested to arise from localized atomic phosphorus. A model idea for explaining the individual temperature dependence of the Fano resonances is presented.