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We present a survey for dense material around young IRAS sources in the Perseus molecular cloud complex in the NH$_3$ (J,K) = (1,1) line at 1.3 cm. NH$_3$ emission was detected in eight, and mapped in seven, out of ten positions chosen for study. The dense cores found typically have lower masses and narrower linewidths than cores previously studied in Perseus, and are located near sources of lower luminosity. NH$_3$ cores are found throughout the Perseus complex; however, much of the detected dense gas is concentrated into two filamentary ``ridges'' located in the western part. As group, NH$_3$ cores in Perseus have mean linewidth 0.6 kms$^{-1}$, radius 0.12 pc, kinetic temperature 13 K, and mass 9 M$_\odot$. These mean values are larger than the mean values for NH$_3$ cores with associated stars in Taurus, but smaller than the mean values for cores associated with stars in Orion A. Some of the cores in Perseus are ``thermally-dominated,'' with thermal and nonthermal linewidths similar to most Taurus cores, while others are ``nonthermally-dominated,'' and are more similar to the cores in Orion A. We conclude that the Perseus complex is intermediate in its star forming potential betweeen the predominantly low-mass star producing regions like Taurus and the regions capable of the producing high mass stars such as Orion A.
