  We determine the most general form of off-shell N=(1,1) supergravity field
configurations in three dimensions by requiring that at least one off-shell
Killing spinor exists. We then impose the field equations of the topologically
massive off-shell supergravity and find a class of solutions whose properties
crucially depend on the norm of the auxiliary vector field. These are
spacelike-squashed and timelike-stretched AdS_3 for the spacelike and timelike
norms, respectively. At the transition point where the norm vanishes, the
solution is null warped AdS_3. This occurs when the coefficient of the
Lorentz-Chern-Simons term is related to the AdS radius by $\mu\ell=2$. We find
that the spacelike-squashed AdS_3 can be modded out by a suitable discrete
subgroup of the isometry group, yielding an extremal black hole solution which
avoid closed timelike curves.
