That's a different subject. You were suggesting two versions at once on the small screen. Whether there are licensing arrangements are not, it would just confuse viewers. Both shows would have to deal with the actors being compared to one another, the character interpretations being compared, and one of them is going to come out on the losing end.
Add to that the ancillary things like the League of Assassins, Lazarus Pits, Talia - some of which show up in one show but not the other, some having different stories and abilities than the other....it would be a terrible idea. Batman has a rich enough gallery that Gotham doesn't need to bring a character into it that's already in use elsewhere.