  We consider the timelike version of Warped Anti-de Sitter space (WAdS), which
corresponds to the three-dimensional section of the G\"{o}del solution of
four-dimensional cosmological Einstein equations. This geometry presents closed
timelike curves (CTCs), which are inherited from its four-dimensional
embedding. In three dimensions, this type of solutions can be supported without
matter provided the graviton acquires mass. Here, among the different ways to
consistenly give mass to the graviton in three dimensions, we consider the
parity-even model known as New Massive Gravity (NMG). In the bulk of timelike
WAdS$_{3}$ space, we introduce defects that, from the three-dimensional point
of view, represent spinning massive particle-like objects. For this type of
sources, we investigate the definition of quasi-local gravitational energy as
seen from infinity, far beyond the region where the CTCs appear. We also
consider the covariant formalism applied to NMG to compute the mass and the
angular momentum of spinning particle-like defects, and compare the result with
the one obtained by means of the quasi-local stress-tensor. We apply these
methods to special limits in which the WAdS$_3$ solutions coincide with locally
AdS$_3$ and locally AdS$_{2}\times \mathbb{R}$ spaces. Finally, we make some
comments about the asymptotic symmetry algebra of asymptotically WAdS$_3$
spaces in NMG.
