  While researchers commonly use the bootstrap for statistical inference, many
of us have realized that the standard bootstrap, in general, does not work for
Chatterjee's rank correlation. In this paper, we provide proof of this issue
under an additional independence assumption, and complement our theory with
simulation evidence for general settings. Chatterjee's rank correlation thus
falls into a category of statistics that are asymptotically normal but
bootstrap inconsistent. Valid inferential methods in this case are Chatterjee's
original proposal (for testing independence) and Lin and Han (2022)'s analytic
asymptotic variance estimator (for more general purposes).
