We theoretically investigate the Goos-Hänchen (GH) shifts of reflected light beams in Thue-Morse photonic crystals. The systems are constituted by two Thue-Morse dielectrics multilayers and satisfy parity-time (PT) symmetry. Double coherent perfect absorption laser points (CPA-LPs) are achieved in the parameter space composed of the incident angle and the gain-loss factor. Dramatic changes in the phase of reflection coefficient induce giant positive and negative spatial GH shifts at the CPA-LPs, while great angular GH shifts exist around the exceptional points (EPs). The spatial GH shifts present non-reciprocity for the forward and backward incident light waves near the double CPA-LPs, while the angular GH shifts are quasi-reciprocal. Increasing the Thue-Morse sequence number, these characteristics are approved around multiple CPA-LPs as well. Our work could pave the way to explore high-accuracy optical sensors.