We report the millimeter-wave radio observations of molecular cloud cores in Taurus. The observed line is the N2H+ emission at 93 GHz, which is known to be less affected by molecular depletion. We have compared starless (IRAS-less) cores with star-forming cores. We found that there is no large difference between starless and star-forming cores, in core radius, linewidth, core mass, and radial intensity profile. Our result is in contrast with the result obtained by using a popular molecular line, in which starless cores are larger and less condensed. We suggest that different results mainly come from whether the employed molecular line is affected by depletion or not. We made a virial analysis, and found that both starless and star-forming cores are not far from the critical equilibrium state, in Taurus. Together with the fact that Taurus cores are almost thermally supported, we conclude that starless Taurus cores evolve to star formation without dissipating turbulence. The critical equilibrium state in the virial analysis corresponds to the critical Bonnor-Ebert sphere in the Bonnor-Ebert analysis (Nakano 1998). It is suggested that the initial condition of the molecular cloud cores/globules for star formation is close to the critical equilibrium state/critical Bonnor-Ebert sphere, in the low-mass star forming region.