The motion of a single hole in a (Formula presented) model for the two-dimensional spin-gap compound (Formula presented) is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a Néel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the interdimer hopping parameters we find a crossover between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the Néel-ordered phase is also briefly considered.