Multicolour broad-band transit observations offer the opportunity to characterize the atmosphere of an extrasolar planet with small- to medium-sized telescopes. One of the most favourable targets is the hot Jupiter HAT-P-32 b. We combined 21 new transit observations of this planet with 36 previously published light curves for a homogeneous analysis of the broad-band transmission spectrum from the Sloan u' band to the Sloan z' band. Our results rule out cloud-free planetary atmosphere models of solar metallicity. Furthermore, a discrepancy at reddest wavelengths to previously published results makes a recent tentative detection of a scattering feature less likely. Instead, the available spectral measurements of HAT-P-32 b favour a completely flat spectrum from the near-UV to the near-IR. A plausible interpretation is a thick cloud cover at high altitudes.