We study distributions of the partition function zeros in the complex temperature plane for a square-lattice homopolymer with nearest-neighbor (NN) and next-nearest-neighbor
 (NNN) interactions. The dependence of distributions on the ratio of NN and NNN interaction strengths R is examined. The finite-size scaling of the zeros is performed to 
obtain the crossover exponent, which is shown to be independent of R within error bars, suggesting that all of these models belong to the same universality class. The 
transition temperatures are also computed by the zeros to obtain the phase diagram, and the results confirm that the model with stronger NNN interaction exhibits stronger
 effects of cooperativity.