Recently, it has been reported that CeFeAsO belongs to orthorhombic structure where both Fe and Ce moments order antiferromagnetically around 140K and 4K, respectively, whereas Ce ions in CeFePO possessing tetragonal structure are in paramagnetic heavy fermion state that lies close to ferromagnetic instability. Investigations on CeFeAs1-xPxO system reveal an antiferromagnetic and ferromagnetic quantum phase transitions around x~0.37 and x~0.92 for the Fe-3d and Ce-4f electrons, respectively. This suggests an emergence of an intermediate ferromagnetic phase in between those two quantum critical points (QCP). To understand the phase transition across QCP, we propose to investigate the local hyperfine fields at the muon site as a function of temperature in polycrystalline CeFeAs1-xPxO (x ¿ 0, 0.04, 0.2, 0.37, 0.7, 0.92, 1.0) system using muon spin resonance technique.