Most employers that I've consulted for had a strict policy against such relationships - stated specifically in employee handbooks.
And if a relationship like this did happen, one of the persons involved had to transfer to another department/division/branch etc, based on the position of the supervisor.
If no transfer position was available, one of the involved would have to voluntarily resign their position. If they chose not to resign, one or both were released from their duties.
The reasons for this type of policy are many, including the morale of co-workers, the implication of favoritism, etc etc. - everything that's currently happening with Parent and her partner.
It figures that it's the policy of a public funded entity to ignore what is common sense in business...