Future seasons of Supergirl could crossover with CW’s Arrow and The Flash, exec producer Greg Berlanti has confirmed.
While there are no current plans for an inter-network crossover event, Berlanti hinted that Supergirl could eventually interact with its sibling series providing the show is successful, per Assignment X:
Right now, there are no plans to do it. Obviously, in success, who knows? The other thing is that, on Arrow or Flash we’ve never mentioned that there’s Superman flying around, and in Supergirl, obviously, Superman is flying around. So that would be one thing we would have to figure out and address down the line. But we’re far away from any of that.