Observations of Centaurus X-3 were made by the University of Durham Mark 6 telescope over a three year period from 1997 to 1999. A detailed timing analysis of the observations has been performed. A search for modulation of the $γ$-ray signal at the pulsar orbital period, as well as for any short-term (few hours) episodes of $γ$-ray emission with a periodicity near, but not necessarily coincident with, the period of X-ray pulsations has been carried out. The results are presented in the context of several possible emission scenarios.