Multiplicative property of the twisted Reidemeister torsion on the connected sum of compact $3$-manifolds

Let M be a $3$-manifold with connected non-vacuos boundary which is not spherical. Assume that N is another $3$-manifold with vacuous boundary and N^ is the $3$-manifold obtained by removing from N the interior of a $3$-cell. In the present paper, we prove that the twisted Reidemeister torsion of the connected sum $M# N$ can be expressed as the product of the torsions of M and N^. Indeed, we show that the twisted Reidemeister torsion has a multiplicative property on the connected sum of compact $3$-manifolds.