Some companies have policies regulating employee dating, but there's no law against it. However, such relationships can bring up some potential issues which could lead to a lawsuit.
For example, they could lead to allegations of discrimination against the other employees. Perhaps there are three employees who are up for a potential promotion. One of them is dating the supervisor who has to make the choice. That person gets picked for the promotion.
Now, it may be a legitimate choice. The relationship may not have factored in. However, it can certainly make other employees feel like they've been discriminated against.
That discrimination can work both ways. If the supervisor and the employee were dating and then broke up, and the promotion then went to someone else, that person may feel he or she was discriminated against because of the failed relationship.
Allowing workers to date can also create gray areas. For instance, if a supervisor asks someone who works under him or her to go out, is it innocent, or is the supervisor trying to use that position and power to get dates? What if the person is asked out repeatedly and declines? At what point does it cross the line from a dedicated attempt at a legitimate relationship and into sexual harassment?
This is why a lot of companies say that employees simply aren't allowed to date. When relationships do enter the workplace, though, and when they lead to potential discrimination or sexual harassment, it's important for those who have been victimized to know what legal rights they have.
Source: FindLaw, "Regulating Work Place Romances," accessed June 20, 2017