Sharp melting that has been found for DNA-linked nanostructure systems such as DNA-linked gold nanoparticles enhances the resolution of DNA sequence detection enough to distinguish between a perfect match and single base pair mismatches. One intriguing explanation of the sharp melting involves the cooperative dehybridization of DNA strands between the nanostructures. However, in the DNA-linked gold nanoparticle system, strong optical absorption by the gold nanoparticles hinders the direct observation of cooperativity. Here, with a combination of theory and experiment, we investigate a DNA-linked polymer system in which we can show that the optical profile of the system at 260 nm is directly related to the individual DNA dehybridization profile, providing a clear distinction from other possible mechanisms. We find that cooperativity plays a crucial role in determining both the value of the melting temperature and the shape of the melting profile well away from the melting temperature. Our analysis suggests that the dehybridization properties of DNA strands in confined or dense structures differ from DNA in solution.