  The Johannsen-Psaltis spacetime explicitly violates the no hair theorem. It
describes rotating black holes with scalar hair in the form of parametric
deviations from the Kerr metric. In principle, black hole solutions in any
modified theory of gravity could be written in terms of the Johannsen-Psaltis
metric. We study the accretion of gas onto a static limit of this spacetime. We
utilise a recently proposed pseudo-Newtonian formulation of the dynamics around
arbitrary static, spherically symmetric spacetimes. We obtain a potential that
generalises the Paczy\'nski-Wiita potential to the static Johannsen-Psaltis
metric. We also perform a fully relativistic analysis of the geodesic equations
in the static Johannsen-Psaltis spacetime. We find that positive values of the
scalar hair parameter, $\epsilon_{3}$, lower the accretion rate and vice versa.
Similarly, positive (negative) values of $\epsilon_{3}$ reduce (increase) the
gravitational acceleration of radially infalling massive particles.
