  A single master equation is given describing spin $s\le2$ test fields that
are gauge- and tetrad-invariant perturbations of the {\it spinning C metric}
spacetime representing a source with mass $M$, uniformly rotating with angular
momentum per unit mass $a$ and uniformly accelerated with acceleration $A$.
This equation can be separated into its radial and angular parts. The behavior
of the radial functions near the horizons is studied and used to examine the
influence of $A$ on the phenomenon of superradiance, while the angular equation
leads to modified spin-weighted spheroidal harmonic solutions generalizing
those of the Kerr spacetime. Finally the coupling between the spin of the
perturbing field and the acceleration parameter $A$ is discussed.
