P 31 nuclear-magnetic-resonance (NMR) studies have been performed in trimer spin chain compound Ca3 CuNi2 (PO4) 4, in the temperature range 4-300 K. In the range 16-300 K, the spectrum corresponds to a typical overlap of two powder patterns, consistent with two inequivalent phosphorous sites, having different shift parameters. A comparison of the isotropic hyperfine field (H hf iso) and the axial part (H hf ax) obtained in the paramagnetic phase of Ca3 CuNi2 (PO4) 4, with those obtained in Ca3 Cu3 (PO4) 4, suggest a stronger interchain exchange interaction in Ca3 CuNi2 (PO4) 4, which is possibly the reason for the higher antiferromagnetic transition temperature in Ca3 CuNi2 (PO4) 4. The temperature dependence of the spin-lattice relaxation rate (1/ T1) shows a clear signature of long-range magnetic order in Ca3 CuNi2 (PO4) 4 below 16 K (TN). TN agrees quite satisfactorily with that obtained from the derivative of the molar susceptibility versus T plot. The NMR line shape below TN shows the signature of a considerable distribution of the internal magnetic field in the ordered state with the existence of two magnetic sublattices with opposite direction of polarization with respect to the direction of the external magnetic field. A comparison of the behavior of the 1/ T1 data in Ca3 CuNi2 (PO4) 4 with those in Sr3 Cu3 (PO4) 4 clearly suggests that the mechanism of the relaxation changes from a two magnon-mediated Raman process in the former to a three magnon-mediated process in the latter. {\textcopyright} 2010 The American Physical Society.