We investigated the Cu-spin correlation in the overdoped regime of the electron-doped high-Tc cuprate thin films of La_2-x_Ce_x_CuO_4_, changing the reduction condition from muon spin relaxation using low-energy muons. The Cu-spin correlation developed at low temperatures for optimally reduced films with x=0.13 as well as x=0.17 where the superconductivity was almost suppressed. These results are contrary to those observed in the hole-doped high-Tc cuprates where the development of the antiferromagnetic Cu-spin correlation disappears together with the suppression of superconductivity. The Cu-spin correlation developed at low temperatures in x=0.17 may be understood in terms of antiferromagnetism, but it may be related to a ferromagnetic order recently suggested in the nonsuperconducting heavily overdoped La$2-x_Ce_x_CuO_4 with x~0.18.

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