In the present work, whenever the response variables are binary, we frame an adaptive allocation rule for a two-treatment two-period crossover design in the presence of possible carry-over effects. The proposed rule is a combination of the play-the-winner and randomized play-the-winner rules. We study various properties of the proposed rule through asymptotics and simulations. Some related inferential problems are also considered. The proposed procedure is compared with some possible competitor. © 2012 Copyright Taylor and Francis Group, LLC.