Causal Dynamical Triangulations (CDT) is a non-perturbative lattice approach to quantum gravity where one assumes space-time foliation into spatial hyper-surfaces of fixed topology. Most of the previous studies of CDT were done for the fixed spatial topology of the 3-sphere. We present recent results for the fixed spatial topology of the 3-torus. We argue that the topology change does neither affect the phase structure nor the order of the phase transitions. Thus, the CDT properties seem to be universal, independently of the spatial topology choice.