When cohort matching (I'm thinking specifically of either propensity score matching or Mahalanobis distance matching), is it appropriate to include the same covariate(s) in both the matching and the final outcome models? Or can you only include a covariate in either the matching model or final model, but not both? In other words, if I include a covariate in both models, am I over-controlling for that covariate?
You should totally include the covariates in both the matching procedure and the outcome model. This approach is called the "doubly robust" approach and is encouraged by most propensity score researchers. Ho, Imai, King, & Stuart (2007) provide good justification for this technique.