We investigate the impact of baseline covariates on the efficiency of statistical analyses of crossover designs. For practical considerations, we contemplate two different baseline methods: study baselines and period-dependent baselines. For each baseline method, we establish analytical upper bounds for the relative efficiency of a large class of crossover designs, the totally balanced designs, under a model with the baseline covariates as compared with the model without the baseline covariates. We present numerical details based on these bounds for assorted scenarios and reveal implications of these results. Copyright © 2012 John Wiley & Sons, Ltd.