We consider the motion of an aspherical inelastic particle of dumbbell type bouncing repeatedly on a horizontal flat surface. The coefficient of restitution of such a particle depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision whose variance is considerable, even for small eccentricity. Assuming random angular orientation of the particle at the instant of contact we characterize the measured coefficient of restitution as a fluctuating quantity and obtain a wide probability density function including a finite probability for negative values of the coefficient of restitution. This may be understood from the partial exchange of translational and rotational kinetic energy.