The pressure-induced magnetic-nonmagnetic transition in a stoichiometric compound Ce7Ni3 was investigated using measurements of the specific heat C and the magnetic susceptibility χ on single crystals down to 0.07 K. The results show that the Ne?el temperature TN decreases linearly with increasing pressure, and vanishes at Pc=0.39 GPa. At 0.36 GPa < Pc, the Cm/T curve deviates strongly from -lnT dependence below 0.5 K, and exhibits a broad maximum around 0.15 K. At 0.43 GPa > Pc, while, on the other hand, a T-independent behavior appears below 0.2 K. These findings indicate that the -lnT dependence observed near Pc between 0.5 and 6 K is a crossover phenomenon to a Fermi-liquid ground state. However, the continuous increase of χ down to 0.09 K at 0.43 GPa is at variance with conventional Fermi-liquid theory.