In this paper, we study the stochastic resonance in a piecewise nonlinear system driven by a periodic signal and colored noises, which is described by multiplicative and additive colored noises with colored cross-correlation. Using the two-state theory and the unified colored approximation, we can derive the analytical expressions of the steady-state probability density and the signal-to-noise ratio (SNR). Effects of colored noises and the periodic signal on SNR are presented. It is found that the conventional stochastic resonance and bona-fide stochastic resonance may exist in this system. Moreover, the value of the SNR peak decreases with increasing correlation time and correlation between the additive and multiplicative noises.