  The hyperfine coupling constants of neutron deficient $^{37}$Ca were deduced
from the atomic hyperfine spectrum of the $4s~^2S_{1/2}$ $\leftrightarrow$
$4p~^2P_{3/2}$ transition in Ca II, measured using the collinear laser
spectroscopy technique. The ground-state magnetic-dipole and spectroscopic
electric-quadrupole moments were determined for the first time as $\mu =
+0.7453(72) \mu_N$ and $Q = -15(11)$ $e^2$fm$^2$, respectively. The
experimental values agree well with nuclear shell model calculations using the
universal sd model-space Hamiltonians versions A and B (USDA/B) in the
$sd$-model space with a 95\% probability of the canonical nucleon
configuration. It is shown that the magnetic moment of $^{39}$Ca requires a
larger non-$sd$-shell component than that of $^{37}$Ca for good agreement with
the shell-model calculation, indicating a more robust closed sub-shell
structure of $^{36}$Ca at the neutron number $N$ = 16 than $^{40}$Ca. The
results are also compared to valence-space in-medium similarity renormalization
group calculations based on chiral two- and three-nucleon interactions.
