  The existing solutions to the Einstein equations describing rotating
cylindrical wormholes are not asymptotically flat and therefore cannot describe
wormhole entrances as local objects in our Universe. To overcome this
difficulty, flat asymptotic regions are added to wormhole solutions by matching
them at some surfaces $\Sigma_-$ and $\Sigma_+$. It is shown, however, that if
the wormhole solution is obtained for scalar fields with arbitrary potentials,
possibly interacting with an azimuthal electric or magnetic field, then the
matter content of one or both thin shells appearing on $\Sigma_-$ and
$\Sigma_+$ violate the Null Energy Condition. Thus exotic matter is still
necessary for obtaining a twice asymptotically flat wormhole.
