We present progress on the synthesis of semimetal Cd3As2 by metal–organic chemical-vapor deposition (MOCVD). Specifically, we have optimized the growth conditions needed to obtain technologically useful growth rates and acceptable thin-film microstructures, with our studies evaluating the effects of varying the temperature, pressure, and carrier-gas type for MOCVD of Cd3As2 when performed using dimethylcadmium and tertiarybutylarsine precursors. In the course of the optimization studies, exploratory Cd3As2 growths are attempted on GaSb substrates, strain-relaxed InAs buffer layers grown on GaSb substrates, and InAs substrates. Notably, only the InAs-terminated substrate surfaces yield desirable results. Extensive microstructural studies of Cd3As2 thin films on InAs are performed by using multiple advanced imaging microscopies and x-ray diffraction modalities. The studied films are 5–75 nm in thickness and consist of oriented, coalesced polycrystals with lateral domain widths of 30–80 nm. The most optimized films are smooth and specular, exhibiting a surface roughness as low as 1.0 nm rms. Under cross-sectional imaging, the Cd3As2-InAs heterointerface appears smooth and abrupt at a lower film thickness, ~30 nm, but becomes quite irregular as the average thickness increases to ~55 nm. The films are strain-relaxed with a residual biaxial tensile strain (εxx = +0.0010) that opposes the initially compressive lattice-mismatch strain of Cd3As2 coherent on InAs (εxx = −0.042). Importantly, phase-identification studies find a thin-film crystal structure consistent with the P42/nbc space group, placing MOCVD-grown Cd3As2 among the Dirac semimetals of substantial interest for topological quantum materials studies.