Since the Arrowverse has already established the existence of the DC Multiverse, there's no telling if Batwoman will hail from Green Arrow and The Flash's Earth-1, Supergirl's Earth-38, or another Earth altogether. We know Bruce Wayne exists on Earth-1 thanks to Oliver Queen name-dropping his fellow businessman during a press conference, and we know Batman is active on Earth-38 thanks to a few mentions of Superman's dark and brooding vigilante friend. It would make perfect sense, then if we learn Kate comes from either of these Earths.
Of the two, it would make more sense to see Kate Kane become active on Earth-38. After all, this is a world that showcases its female heroes like no other, and it's also one where Maggie Sawyer, Batwoman's longtime girlfriend in the source material, exists as a major character. Batman is active on this Earth, so Batwoman being pre-established but not yet mentioned would make sense as well. And though they haven't met (to our knowledge), Kate calling on Kara Zor-El for help would be as solid a way to bring Batwoman into the next Arrowverse crossover as anything.
"Crisis on Earth-X," the last Arrowverse crossover, was a spectacular affair that involved a third, not so pleasant Earth. Since Stephen Amell said that the upcoming crossover would be smaller in scale, we don't see yet another Earth factoring into the proceedings. Rather, we expect that Batwoman is already be kicking bad guys's butts and jumping off of rooftops on Supergirl's Earth 38. The Melissa Benoist-fronted series is the perfect place to launch the character, and for her to have a continued presence on after having her mix up with the rest of the extensive cast of all four superhero series.
The next Arrowverse crossover will once again bring characters from Arrow, The Flash, Legends of Tomorrow and Supergirl on the screen together for one big comic book-inspired adventure. The television event is expected to air late in the fall.