  We analyze two dedicated NuSTAR observations with exposure ${\sim}190$ ks
located ${\sim}10^\circ$ from the Galactic plane, one above and the other
below, to search for x-ray lines from the radiative decay of sterile-neutrino
dark matter. These fields were chosen to minimize astrophysical x-ray
backgrounds while remaining near the densest region of the dark matter halo. We
find no evidence of anomalous x-ray lines in the energy range 5--20 keV,
corresponding to sterile neutrino masses 10--40 keV. Interpreted in the context
of sterile neutrinos produced via neutrino mixing, these observations provide
the leading constraints in the mass range 10--12 keV, improving upon previous
constraints in this range by a factor ${\sim}2$. We also compare our results to
Monte Carlo simulations, showing that the fluctuations in our derived limit are
not dominated by systematic effects. An updated model of the instrumental
background, which is currently under development, will improve NuSTAR's
sensitivity to anomalous x-ray lines, particularly for energies 3--5 keV.
