  In this paper, Ricci-inverse gravity is investigated. It is an alternative
theory of gravity that introduces into the Einstein-Hilbert action an
anti-curvature scalar that is obtained from the anti-curvature tensor which is
the inverse of the Ricci tensor. An axially symmetric spacetime with causality
violation is studied. Two classes of the model are discussed. Different sources
of matter are considered. Then a direct relation between the content of matter
and causality violation is shown. Our results confirm that Ricci-inverse
gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the
violation of causality. Furthermore, a comparison is made between the results
of general relativity and Ricci-inverse gravity. Other spacetimes, such as
G\"{o}del and G\"{o}del-type universes, which are exact solutions of general
relativity and allow for causality violations, are also explored in
Ricci-inverse gravity framework.
