A review of the Flash Arrow Crossover 2 [spoilers for both episodes]

[Tonguez]

Regardless of channels, I think Supergirl is set up as a different universe. In the Arrowverse, metahumans are a fairly new thing, at least in the public eye. In Supergirl, Superman has been around for quite a while, and has an established history of fighting other supers (e.g. "Not even Superman could defeat Reactron!")

they are different universes and CBS President Nina Tassler has said "Well, those two shows [The Flash and Arrow] are on a different network...So I think we'll keep Supergirl to ourselves for awhile."

apparently the shows may be sharing the same multiverse which is good since The Flash has set that up that mechanic. but the speculation is they wont crossover in Supergirls first season or two - but it is a suggestion for far future seasons (CW is actually part owned by CBS)