Writer and Producer Greg Berlanti has quite a few superhero shows under his belt, including Arrow, The Flash, and the upcoming Supergirl, as well as executive producing DC's Legends of Tomorrow, the Arrow/The Flash spin-off. He recently talked to Variety about the all of his shows and said this about Supergirl crossing-over with the CW super-hero shows:
“The network has said publicly at this point they’re going to keep her to themselves... I always approach the shows as a fan first, so I would love to see (a crossover). I think in success, all things are possible. But there’s a lot that would have to happen before everybody might say yes to that.”
It's a bit early to have Supergirl cross-over, for a few reasons. While CBS and the CW do have ties, they are separate networks and operate as such. In addition, unlike The Flash, where Barry was first introduced in Arrow, there are no ties between the characters within Supergirl and either of the CW shows. While CBS said that they're keeping Supergirl to themselves, don't count a future crossover out completely, just yet. CBS may be a bit more guarded about the property. Just because comic book shows are a hit on the CW doesn't mean CBS will have the same success.
While now it looks a little bleak, don't count a major cross-over out just yet, but the chances of seeing any of that in season one of Supergirl is slim to none, with it leaning heavily to none.
For now, we just have this: