Frequentists' inference often delivers point estimators associated with con dence intervals
or sets for parameters of interest. Constructing the con dence intervals or sets requires understanding
the sampling distributions of the point estimators, which, in many but not all cases, are
related to asymptotic Normal distributions ensured by central limit theorems. Although previous
literature has established various forms of central limit theorems for statistical inference in
super population models, we still need general and convenient forms of central limit theorems
for some randomization-based causal analysis of experimental data, where the parameters of
interests are functions of a nite population and randomness comes solely from the treatment
assignment. We use central limit theorems for sample surveys and rank statistics to establish
general forms of the nite population central limit theorems that are particularly useful for
proving asymptotic distributions of randomization tests under the sharp null hypothesis of zero
individual causal e ects, and for obtaining the asymptotic repeated sampling distributions of the
causal e ect estimators. The new central limit theorems hold for general experimental designs
with multiple treatment levels, multiple treatment factors and vector outcomes, and are immediately
applicable for studying the asymptotic properties of many methods in causal inference,
including instrumental variable, regression adjustment, rerandomization, clustered randomized
experiments, and so on. Previously, the asymptotic properties of these problems are often based
on heuristic arguments, which in fact rely on general forms of nite population central limit
theorems that have not been established before. Our new theorems ll in this gap by providing
more solid theoretical foundation for asymptotic randomization-based causal inference.