We present the design, fabrication, and feedforward control of a insect-sized (142 mg) aerial robot that is equipped with a bio-inspired inertial tail. A tail allows the robot to perform rapid inertial reorientation as well as to shift weight to modulate aerodynamic torques on its body. Here we present the first analysis of inertial reorientation using a piezo actuator, departing from previous work to date that has focused exclusively on actuation by DC electric motor. The primary difference is that unlike a geared motor system, the piezo-tail system operates as a resonant system, exhibiting slowly-decaying oscillations. We present a dynamic model of piezo-driven inertial reorientation, along with an open-loop feedforward controller that reduces excitation of the resonant mode. We validate our approach on a tethered testbed as well as a flight-capable prototype. Our results indicate that incorporating a tail can allow for more rapid dynamic maneuvers and could stabilize the robot during flight.