We present Monte Carlo simulations of dissociation of duplexes formed of complementary single-stranded DNAs with one of the strands attached to the surface. To describe the transition from the bound state to the unbound state of two strands located nearby, we use a lattice model taking DNA base-pair interactions and comformational changes into account. The results obtained are employed as a basis for a more coarse-grained model including strand backward association and diffusion resulting in complete dissociation. The distribution of the dissociation time is found to be exponential. This finding indicates that the non-exponential kinetic features observed in the corresponding experiments seem to be related to extrinsic factors, e.g., to the surface heterogeneity.