No, you do not need to file a K-1 if there was no distribution.
From tagteam: "The fiduciary is not required to prepare and file K-1s when distributions of income have not actually been made and distributions of income are not deemed to have been made (even though no distributions have been actually made).
It is, however, considered by some to be good practice to issue "zero K-1s" to beneficiaries in order to make them aware that they have no individual reporting requirement for that tax year from the trust."