We present B-, V-, R_c-, I_c-, J-, H-, K- and K'-band observations of the optical transient (OT) associated with GRB970228, based on a reanalysis of previously used images and unpublished data. In order to minimize calibration differences we have collected and analyzed most of the photometry and consistently determined the magnitude of the OT relative to a set of secondary field stars. We confirm our earlier finding that the early decay of the light curves (before March 6, 1997) was faster than that at intermediate times (between March 6 and April 7, 1997). At late times the light curves resume a fast decay (after April 7, 1997). The early-time observations of GRB970228 are consistent with relativistic blast-wave models but the intermediate- and late-time observations are hard to understand in this framework. The observations are well explained by an initial power law decay with index -1.73 +0.09 -0.12 modified at later times by a type-I_c supernova light curve. Together with the evidence for GRB980326 and GRB980425 this gives further support for the idea that at least some GRBs are associated with a possibly rare type of supernova.