  We describe a laser spectroscopic study of ytterbium monomethoxide,
YbOCH$_3$, a species of interest to searches for time-reversal symmetry
violation using laser-cooled molecules. We report measurements of vibrational
structure in the $\tilde{X}$ and $\tilde{A}$ states, vibrational branching
ratios for several components of the $\tilde{A}$ state, and radiative lifetimes
of low-lying electronic states. $\textit{Ab initio}$ calculations are used to
aid the assignment of vibronic emission bands and provide insight into the
electronic and vibrational structure. Our results demonstrate that rapid
optical cycling is feasible for YbOCH$_3$, opening a path to
orders-of-magnitude increased sensitivity in future measurements of P- and/or
T-violating physics.
