The Compton Spectrometer and Imager (COSI) is a balloon-borne γ-ray (0.2-5 MeV) telescope designed to study astrophysical sources. COSI employs a compact Compton telescope design utilizing 12 highpurity germanium double-sided strip detectors and is inherently sensitive to polarization. In 2016, COSI was launched from Wanaka, New Zealand and completed a successful 46-day flight on NASA's new Super Pressure Balloon. In order to perform imaging, spectral, and polarization analysis of the sources observed during the 2016 flight, we compute the detector response from well-benchmarked simulations. As required for accurate simulations of the instrument, we have built a comprehensive mass model of the instrument and developed a detailed detector effects engine which applies the intrinsic detector performance to Monte Carlo simulations. The simulated detector effects include energy, position, and timing resolution, thresholds, dead strips, charge sharing, charge loss, crosstalk, dead time, and detector trigger conditions. After including these effects, the simulations closely resemble the measurements, the standard analysis pipeline used for measurements can also be applied to the simulations, and the responses computed from the simulations are accurate. We have computed the systematic error that we must apply to measured fluxes at certain energies, which is 6.3% on average. Here we describe the detector effects engine and the benchmarking tests performed with calibrations.