That is, until the episode ‘The Darkest Place’, when Supergirl not only confirmed the existence of Gotham City, but also seemingly, directly confirmed the existence of Batman in the DCTV universe (or Arrow-multiverse, if you prefer).
Since then unfortunately, no other comments or references connecting back to Batman have been made in any of The CW’s DC TV shows.
[SPOILERS for those not caught up on Supergirl ahead.]
Early in season 2, Supergirl surprised fans everywhere when it introduced their its own live-action version of Superman/Clark Kent on Kara’s Earth, leading many fans to speculate about whether or not we will ever see a DCTV version of The Dark Knight.