  Protostellar multiplicity is common at all stages and mass ranges. However,
the factors that determine the multiplicity of protostellar systems have not
been systematically characterized through their molecular gas. Nobeyama 45m
Radio Observatory OTF maps of HCN, HNC, HCO$^+$, and N$_2$H$^+$ (J = 1--0)
toward five subregions in Perseus, complemented with single pointing APEX
observations of HNC (J = 4--3) are used to derive physical parameters of the
dense gas. Both observations have angular resolutions of $\sim$18", equivalent
to $\sim$5000 AU scales at the distance of Perseus. Kinetic gas temperature is
derived from the $I$(HCN)/$I$(HNC) J = 1--0 ratio, and H$_2$ density is
obtained from the HNC J=4--3/J=1--0 ratio. These parameters are used to obtain
the N$_2$H$^+$ and HCO$^+$ gas masses. The inferred and derived parameters are
compared to source parameters. Inferred mean kinetic gas temperature
($I$(HCN)/$I$(HNC) J=1--0 ratio; ranging between 15 and 26 K), and H$_2$
volumetric density (HNC J=4--3/J=1--0; 10$^5$ -- 10$^6$ cm$^{-3}$) do not show
correlations with multiplicity in Perseus. The derived gas and dust masses, 1.3
to 16 $\times~10^{-9}$ M$_{\odot}$ for the N$_2$H$^+$ gas mass, 0.1 to 25
M$_{\odot}$ for envelope dust masses (850 $\mu$m), and 0.8 to 10
$\times~10^{-10}$ M$_{\odot}$ for the HCO$^+$ gas mass, are correlated to
multiplicity and number of protostellar components. The warm gas masses are a
factor of 16 lower than the cold gas masses. This work shows that gas and dust
mass is correlated to multiplicity at $\sim$5000 AU scales in Perseus. Higher
order multiples tend to have higher gas and dust masses in general, while close
binaries (separations $\leq$7") and single protostars have similar gas and dust
mass distributions. On the other hand, H$_2$ density and kinetic gas
temperature do not show any correlation with multiplicity.
