Planning time-optimal trajectories for quadrotors in cluttered environments is a challenging, non-convex problem. This paper addresses minimizing the traversal time of a given collision-free geometric path without violating actuation bounds of the vehicle. Previous approaches have either relied on convex relaxations that do not guarantee dynamic feasibility or have generated overly conservative time parametrizations. We propose TOPPQuad, a time-optimal path parameterization algorithm for quadrotors which explicitly incorporates quadrotor rigid body dynamics and constraints, such as bounds on inputs (including motor thrusts) and state of the vehicle (including the pose, linear and angular velocity and acceleration). We demonstrate the ability of the planner to generate faster trajectories that respect hardware constraints of the robot compared to planners with relaxed notions of dynamic feasibility in both simulation and hardware. We also demonstrate how TOPPQuad can be used to plan trajectories for quadrotors that utilize bidirectional motors. Overall, the proposed approach paves a way towards maximizing the efficacy of autonomous micro aerial vehicles while ensuring their safety.