The Goos-Hanchen (GH) effect for wave scattering from complex PT -symmetric periodic potentials (complex crystals) is theoretically investigated, with specific reference to optical GH shift in photonic crystal slabs with a sinusoidal periodic modulation of both real and imaginary parts of the dielectric constant. The analysis highlights some distinct and rather unique features as compared to the GH shift found in ordinary crystals. In particular, as opposed to GH shift in ordinary crystals, which is large at the band gap edges, in complex crystals the GH shift can be large inside the reflection (amplification) band and becomes extremely large as the PT symmetry-breaking threshold is approached.