We consider a sign-determined Reidemeister torsion with multivariables for a
hyperbolic three-dimensional manifold with cusps. Using a cut and paste
argument, we prove that this Reidemeister torsion is a polynomial invariant
when provided with appropriate conditions on the topology of the manifold and
SL(2, C)-representations of its fundamental group. Under such assumptions, it
is proved that this polynomial invariant is reciprocal like the usual Alexander
polynomial. It is also shown that a differential coefficient of this polynomial
invariant provides the non-acyclic SL(2,C)-Reidemeister torsion. Moreover, we
show a covering formula for a finite abelian covering, which gives the
Reidemeister torsion of a covering space by the product of those of the base
space manifold.