  We address the problem of classifying all N=2 supercurrent multiplets in four
space-time dimensions. For this purpose we consider the minimal formulation of
N=2 Poincare supergravity with a tensor compensator, and derive its linearized
action in terms of three N=2 off-shell multiplets: an unconstrained scalar
superfield, a vector multiplet, and a tensor multiplet. Such an action was
ruled out to exist in the past. Using the action constructed, one can derive
other models for linearized N=2 supergravity by applying N=2 superfield duality
transformations. The action depends parametrically on a constant non-vanishing
real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the
tensor compensator. Upon reduction to N=1 superfields, we show that the model
describes two dually equivalent formulations for the massless multiplet
(1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0,
the action describes (i) new minimal N=1 supergravity; and (ii) the
Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0,
on the other hand, the action describes (i) old minimal N=1 supergravity; and
(ii) the Ogievetsky-Sokatchev gravitino multiplet.
