Yep. There was one early Batman series which revealed that his father had once dressed as a bat-man for a costume party. Batman wore the costume when apprehending a criminal who had done something awful to Batdad and the criminal, seeing the costume thought it was Batdad returned to life and panicked falling to his death.¹

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1. Likely inaccurate description of the plot based on 45-year-old memories of reading the story in a library collection.

The underwear worn outside of the pants are a dead giveaway.