  Nuclear reactions of interest for astrophysics and applications often rely on
statistical model calculations for nuclear reaction rates, particularly for
nuclei far from $\beta$-stability. However, statistical model parameters are
often poorly constrained, where experimental constraints are particularly
sparse for exotic nuclides. For example, our understanding of the breakout from
the NiCu cycle in the astrophysical rp-process is currently limited by
uncertainties in the statistical properties of the proton-rich nucleus
$^{60}$Zn. We have determined the nuclear level density of $^{60}$Zn using
neutron evaporation spectra from $^{58}$Ni($^3$He, n) measured at the Edwards
Accelerator Laboratory. We compare our results to a number of theoretical
predictions, including phenomenological, microscopic, and shell model based
approaches. Notably, we find the $^{60}$Zn level density is somewhat lower than
expected for excitation energies populated in the
$^{59}$Cu(p,$\gamma$)$^{60}$Zn reaction under rp-process conditions. This
includes a level density plateau from roughly 5-6 MeV excitation energy, which
is counter to the usual expectation of exponential growth and all theoretical
predictions that we explore. A determination of the spin-distribution at the
relevant excitation energies in $^{60}$Zn is needed to confirm that the
Hauser-Feshbach formalism is appropriate for the $^{59}$Cu(p,$\gamma$)$^{60}$Zn
reaction rate at X-ray burst temperatures.
