We present a multiplicity study of all known protostars (94) in the Perseus molecular cloud from a Karl G. Jansky Very Large Array (VLA) survey at Ka-band (8 mm and 1 cm) and C-band (4 cm and 6.6 cm). The observed sample has a bolometric luminosity range between 0.1 L$_{odot}$ and $sim$33 L$_{odot}$, with a median of 0.7 L$_{odot}$. This multiplicity study is based on the Ka-band data, having a best resolution of $sim$0.065 (15 AU) and separations out to $sim$43 (10000 AU) can be probed. The overall multiplicity fraction (MF) is found to be of 0.40$pm$0.06 and the companion star fraction (CSF) is 0.71$pm$0.06. The MF and CSF of the Class 0 protostars are 0.57$pm$0.09 and 1.2$pm$0.2, and the MF and CSF of Class I protostars are both 0.23$pm$0.08. The distribution of companion separations appears bi-modal, with a peak at $sim$75 AU and another peak at $sim$3000 AU. Turbulent fragmentation is likely the dominant mechanism on $>$1000 AU scales and disk fragmentation is likely to be the dominant mechanism on $<$200 AU scales. Toward three Class 0 sources we find companions separated by $<$30 AU. These systems have the smallest separations of currently known Class 0 protostellar binary systems. Moreover, these close systems are embedded within larger (50 AU to 400 AU) structures and may be candidates for ongoing disk fragmentation.
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