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I previously applied to, was accepted, and deferred admission to a particular law school. At the end of my deferral period, I requested an additional deferral to complete the work I was doing at the time. This request was turned down and my offer of acceptance was withdrawn.

I am now applying back to schools. Do I need to explain any of this to other schools I apply to?

I'd say it's worthy of an addendum. I don't know if schools can see your history like that, but I can't imagine it would hurt to address it directly.