Carlitz proved a powerful reciprocity theorem for generalized Dedekind-Rademacher sums. Among its many consequences was an interesting polynomial reciprocity theorem which holds under a certain restriction of its parameters. Carlitz remarked that it was unclear how this restriction could be removed. In this paper, we remove this restriction and obtain a generalization of Carlitz’s polynomial reciprocity theorem. As a corollary, we get the polynomial reciprocity theorem of Beck and Kohl.