We present decentralized collision avoidance algorithms for quadrotor swarms operating under uncertain state estimation. Our approach exploits the differential flatness property and feedforward linearization to approximate the quadrotor dynamics and performs reciprocal collision avoidance. We account for the uncertainty in position and velocity by formulating the collision constraints as chance constraints, which describe a set of velocities that avoid collisions with a specified confidence level. We present two different methods for formulating and solving the chance constraints: our first method assumes a Gaussian noise distribution. Our second method is its extension to the non-Gaussian case by using a Gaussian Mixture Model (GMM). We reformulate the linear chance constraints into equivalent deterministic constraints, which are used with an MPC framework to compute a local collision-free trajectory for each quadrotor. We evaluate the proposed algorithm in simulations on benchmark scenarios and highlight its benefits over prior methods. We observe that both the Gaussian and non-Gaussian methods provide improved collision avoidance performance over the deterministic method. On average, the Gaussian method requires ~5ms to compute a local collision-free trajectory, while our non-Gaussian method is computationally more expensive and requires ~9ms on average in scenarios with 4 agents.