63Cu nuclear quadrupole resonance (NQR) has been observed in a heavy-fermion system CeCu2Si2 for three difference samples. The NQR measurements in CeCu2Si2 show strong sample dependence in spin-lattice relaxation and superconducting transition temperature Tc. In two superconducting CeCu2Si2 specimens, NQR experiments have revealed an onset of a phase transition below ~1 K. Zero- and longitudinal-field muon-spin-relaxation measurements suggest an static magnetic ordering below ~0.8 K either in the spinglass or in incommensurate spin-density-wave states. The exotic transition observed in NQR measurements should be closely related to the static magnetic ordering in muon-spin-relaxation measurements. By Kato-Machida theory, the most possible electron-electron pairs in CeCu2Si2 are anisotropic s-wave pairing with (0, E) and p-wave pairing with (O,,, 0). The sample dependence in CeCu2Si2 is due to the competition of anisotropic s-wave pairing and p-wave pairing. NQR data from a nonsuperconducting CeCu2Si2 sample are consistent with the extensive disorder in Cu site occupation. Therefore, the spin-density wave may be depressed in the nonsuperconducting CeCu2Si2. The superconducting transition temperature Tc can be enhanced by the presence of spin-density wave such that, if the spin-density wave is depressed, CeCu2Si2 will lose the superconductivity.