Statistical analyses of crossover clinical trials have mainly focused on assessing the treatment effect, carryover effect, and period effect. When a treatment‐by‐period interaction is plausible, it is important to test such interaction first before making inferences on differences among individual treatments. Considerably less attention has been paid to the treatment‐by‐period interaction, which has historically been aliased with the carryover effect in two‐period or three‐period designs. In this article, from the data of a newly developed four‐period crossover design, we propose a statistical method to compare the effects of two active drugs with respect to two response variables. We study estimation and hypothesis testing considering the treatment‐by‐period interaction. Constrained least squares is used to estimate the treatment effect, period effect, and treatment‐by‐period interaction. For hypothesis testing, we extend a general multivariate method for analyzing the crossover design with multiple responses. Results from simulation studies have shown that this method performs very well. We also illustrate how to apply our method to the real data problem.