While the official word from CBS in the past has been that they want to establish Supergirl as its own show before worrying about crossovers with other DC Comics shows, a new rumor suggests that CBS might now be moving forward with crossover plans.
According to Bleeding Cool, they have been told by a reliable source that Supergirl and The Flash crossover plans are in the works. According to their source, Supergirl was initially ordered for thirteen episodes with an option for nine more to complete a twenty-two episode season.
Supergirl initially started off with super ratings when it premiered after The Big Bang Theory. However, the show has dipped somewhat in the ratings after losing The Big Bang Theory lead-in. A crossover with The Flash could provide Supergirl a ratings boost during May sweeps.