The phrase "Did I do that?" is famously associated with the character Steve Urkel from the American sitcom Family Matters. It is Steve Urkel's catchphrase, often said after he causes some mishap or trouble, highlighting his clumsy and nerdy character traits.
So, if the question "did I do that?" is a playful or humorous reference, it relates to Steve Urkel's iconic line from Family Matters, where he acknowledges causing an accident or problem with this memorable expression.