  In a very recent work, G. E. Andrews defined the combinatorial objects which
he called {\it singular overpartitions} with the goal of presenting a general
theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan
type for ordinary partitions with restricted successive ranks. As a small part
of his work, Andrews noted two congruences modulo 3 which followed from
elementary generating function manipulations. In this work, we prove that
Andrews' results modulo 3 are two examples of an infinite family of congruences
modulo 3 which hold for that particular function. We also expand the
consideration of such arithmetic properties to other functions which are part
of Andrews' framework for singular overpartitions.
