Zero- and longitudinal-field muon-spin-relaxation (ZF- and LF-mu SR) measurements were carried out on the impurity-doped spin gap systems TlCu1-xMgxCl3. In a slightly doped case of x = 0.0047, no evidence for a static internal magnetic field was observed down to 20 mK although the specific heat indicated the magnetic phase transition at T = 0.70 K as previously reported [J. Phys. Soc. Jpn. 78, 074705 (2009)]. Above x = 0.006, the existence of a static internal magnetic field is confirmed by LF-mu SR, and with increasing Mg concentration of x, the internal magnetic field, and the volume fraction of a spin frozen region where the static internal magnetic field appears increase simultaneously. These results suggest that the magnetic ground state changes from the spin singlet state to a spin fluctuating state, and to a spin frozen state by the impurity doping, and also suggest there exist a threshold doping ratio in the appearance of a static staggered moment in the S = 1/2 dimer systems weakly coupled by three-dimensional interactions.