  We propose a new off-shell formulation for N-extended conformal supergravity
in three spacetime dimensions. Our construction is based on the gauging of the
N-extended superconformal algebra in superspace. Covariant constraints are
imposed such that the algebra of covariant derivatives is given in terms of a
single curvature superfield which turns out to be the super Cotton tensor. An
immediate corollary of this construction is that the curved superspace is
conformally flat if and only if the super Cotton tensor vanishes. Upon
degauging of certain local symmetries, our formulation is shown to reduce to
the conventional one with the local structure group SL(2,R) x SO(N).
