  This paper establishes a combinatorial central limit theorem for stratified
randomization, which holds under a Lindeberg-type condition. The theorem allows
for an arbitrary number or sizes of strata, with the sole requirement being
that each stratum contains at least two units. This flexibility accommodates
both a growing number of large and small strata simultaneously, while imposing
minimal conditions. We then apply this result to derive the asymptotic
distributions of two test statistics proposed for instrumental variables
settings in the presence of potentially many strata of unrestricted sizes.
