  We present a sample of 10 low-mass active galactic nuclei (AGNs) selected
from the 40-month NuSTAR serendipitous survey. The sample is selected to have
robust NuSTAR detections at $3 - 24$~keV, to be at $z < 0.3$, and to have
optical r-band magnitudes at least 0.5~mag fainter than an $L_\star$ galaxy at
its redshift. The median values of absolute magnitude, stellar mass and 2--10
X-ray luminosity of our sample are $\langle M_r\rangle = -20.03$, $\langle
M_\star\rangle = 4.6\times10^{9}M_\odot$, and $\langle
L_{2-10\mathrm{keV}}\rangle = 3.1\times10^{42}$ erg s$^{-1}$, respectively.
Five objects have detectable broad H$\alpha$ emission in their optical spectra,
indicating black-hole masses of $(1.1-10.4)\times 10^6 M_\odot$. We find that
$30^{+17}_{-10}\%$ of the galaxies in our sample do not show AGN-like optical
narrow emission lines, and one of the ten galaxies in our sample,
J115851+4243.2, shows evidence for heavy X-ray absorption. This result implies
that a non-negligible fraction of low-mass galaxies might harbor accreting
massive black holes that are missed by optical spectroscopic surveys and $<10$
keV X-ray surveys. The mid-IR colors of our sample also indicate these
optically normal low-mass AGNs cannot be efficiently identified with typical
AGN selection criteria based on WISE colors. While the hard ($>10$ keV) X-ray
selected low-mass AGN sample size is still limited, our results show that
sensitive NuSTAR observations are capable of probing faint hard X-ray emission
originating from the nuclei of low-mass galaxies out to moderate redshift
($z<0.3$), thus providing a critical step in understanding AGN demographics in
low-mass galaxies.
