  This paper studies a class of stationary mean-field games of singular
stochastic control with regime-switching. The representative agent adjusts the
dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular
stochastic control and faces a long-time-average expected profit criterion. The
mean-field interaction is of scalar type and it is given through the stationary
distribution of the population. Via a constructive approach, we prove the
existence and uniqueness of the stationary mean-field equilibrium. Furthermore,
we show that this realizes a symmetric $\varepsilon_N$-Nash equilibrium for a
suitable ergodic $N$-player game with singular controls. The proof hinges on
the characterization of the optimal solution to the representative player's
ergodic singular stochastic control problem with regime switching, which is of
independent interest and appears here for the first time.
