We describe a laser spectroscopic study of ytterbium monomethoxide, a species of interest to search for time-reversal symmetry violation using laser-cooled molecules. We have performed measurements of vibrational structure in the low-lying electronic states, vibrational branching ratios for several electronically excited vibronic states, and radiative lifetimes of low-lying electronic states. In addition, we have recorded the rotationally-resolved high-resolution excitation spectrum of the A ²E_1/2 - X ²A₁ band. Ab initio calculations are used to aid the assignment of vibronic emission bands and provide insight into the electronic and vibrational structure. We compare the structure of YbOCH₃ to the isoelectronic species YbF and YbOH, as well as to the previously studied alkaline-earth monomethoxides. Finally, we discuss how our results open a path to increased sensitivity to P- and/or T-violating physics in future measurements.