The coupling of the translational and rotational Brownian motion of a particle due to its arbitrary geometric shape is studied. The generalized kinetic equation for the Brownian particle distribution function is derived from the Liouville equation. The correlation functions for random force and torque are calculated from hydrodynamic fluctuation theory. It is found that the coupling effect plays an appreciable role in the diffusivities of asymmetric particles. For the special case of a sphere where there is no coupling, the autocorrelation function for the random torque in rotational Brownian motion is given in closed from. Its asymptotic from at large times is proportional to (time)−5/2. As an example of an asymmetric particle, the diffusivity tensor is worked out for two disks connected by a rigid rod.