  We present a new data release from the Fiber Multi-Object Spectrograph
(FMOS)-COSMOS survey, which contains the measurements of spectroscopic redshift
and flux of rest-frame optical emission lines (H$\alpha$, [NII], [SII],
H$\beta$, [OIII]) for 1931 galaxies out of a total of 5484 objects observed
over the 1.7 deg$^2$ COSMOS field. We obtained $H$-band and $J$-band
medium-resolution ($R\sim3000$) spectra with FMOS mounted on the Subaru
telescope, which offers an in-fiber line flux sensitivity limit of $\sim 1
\times 10^{-17}~\mathrm{erg~s^{-1}~cm^{-2}}$ for an on-source exposure time of
five hours. The full sample contains the main population of star-forming
galaxies at $z\sim1.6$ over the stellar mass range $10^{9.5}\lesssim
M_\ast/M_\odot \lesssim 10^{11.5}$, as well as other subsamples of
infrared-luminous galaxies detected by Spitzer and Herschel at the same and
lower ($z\sim0.9$) redshifts and X-ray emitting galaxies detected by Chandra.
This paper presents an overview of our spectral analyses, a description of the
sample characteristics, and a summary of the basic properties of emission-line
galaxies. We use the larger sample to re-define the stellar mass--star
formation rate relation based on the dust-corrected H$\alpha$ luminosity, and
find that the individual galaxies are better fit with a parametrization
including a bending feature at $M_\ast\approx10^{10.2}~M_\odot$, and that the
intrinsic scatter increases with $M_\ast$ from 0.19 to $0.37$ dex. We also
confirm with higher confidence that the massive
($M_\ast\gtrsim10^{10.5}~M_\odot$) galaxies are chemically mature as much as
local galaxies with the same stellar masses, and that the massive galaxies have
lower [SII]/H$\alpha$ ratios for their [OIII]/H$\beta$, as compared to local
galaxies, which is indicative of enhancement in ionization parameter.
