We investigated the structural phase transition occurring around 760 K in a colossal magnetoresistance material, La0.625Ca0.375MnO3. In order to uncover detailed features of this transition between the high temperature rhombohedral (R3c) and the low temperature orthorhombic phase (Pnma), high resolution neutron powder diffraction, resistivity measurements, and elastic constant measurements were carried out up to 1000 K. From the Rietveld refinement analysis of the powder diffraction data, it is shown that the transition is of first order as expected from symmetry and that there exists a temperature region of similar to40 K around the transition temperature where the two phases coexist. This phase coexistence in the transition region accounts for the results of the elastic constant and resistivity measurements. Neutron powder diffraction data also allowed us to determine the tilt angles of the soft lattice modes, R-25 and M-3, relevant to the phase transition.