  The rovibronic (rotation-vibration-electronic) spectrum of the calcium
monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres
and ultracold molecules. Here, we theoretically investigate the
$\tilde{A}\,^2\Pi$--$\tilde{X}\,^2\Sigma^+$ band system of CaOH using
high-level \textit{ab initio} theory and variational nuclear motion
calculations. New potential energy surfaces (PESs) are constructed for the
$\tilde{X}\,^2\Sigma^+$ and $\tilde{A}\,^2\Pi$ electronic states along with
$\tilde{A}$--$\tilde{X}$ transition dipole moment surfaces (DMSs). For the
ground $\tilde{X}\,^2\Sigma^+$ state, a published high-level \textit{ab initio}
PES is empirically refined to all available experimental rovibrational energy
levels up to $J=15.5$, reproducing the observed term values with a
root-mean-square (rms) error of 0.06~cm$^{-1}$. Large-scale multireference
configuration interaction (MRCI) calculations using quintuple-zeta quality
basis sets are employed to generate the $\tilde{A}\,^2\Pi$ state PESs and
$\tilde{A}$--$\tilde{X}$ DMSs. Variational calculations consider both
Renner-Teller and spin-orbit coupling effects, which are essential for a
correct description of the spectrum of CaOH. Computed rovibronic energy levels
of the $\tilde{A}\,^2\Pi$ state, line list calculations up to $J=125.5$, and an
analysis of Renner-Teller splittings in the $\nu_2$ bending mode of CaOH are
discussed.
