I'm assuming you didn't get in, so I'd say not.
I mean, you can use the story again if you really want, but you probably missed the mark on convincing them you were the right fit the first time around, and you also probably don't know concretely what they liked and didn't like about your candidacy. Perhaps it was in the execution of telling the story or in the reflection about what made the story meaningful for you. I personally wouldn't reuse anything. Prove that you've grown AND that you care enough to do a whole new application.
Blogging about the MBA application process. Because I need to do something with all this bschool energy.
http://www.mybreakaway.com/ Recent post: September 20, "Transitions"
Yale School of Management MBA Candidate, 2015.