So, this question is not really about the series the Mentalist, but I think it fits here anyway.
First, I am not from US, so I dont know if CBI really exists or was made up only for the series.
In the series Wayne Rigsby and Grace van Pelt have an hidden relationship because it is not allowed at CBI. Everybody warns them to keep it a secret, because otherwise that would have consequences and one of them would have to leave the CBI.
Is this really a rule at CBI or similar American criminal bureaus? What is the reason for this rule? In Europe I have never heard of such a rule, as far as I know relationships are not forbidden here when working together in a police-like environment.