  We prove a central limit theorem (CLT) for the product of a class of random
singular matrices related to a random Hill's equation studied by
Adams$\unicode{x2013}$Bloch$\unicode{x2013}$Lagarias. The CLT features an
explicit formula for the variance in terms of the distribution of the matrix
entries and this allows for exact calculation in some examples. Our proof
relies on a novel connection to the theory of $m$-dependent sequences which
also leads to an interesting and precise nondegeneracy condition.
