The CW, which is owned by CBS and WB, recently renewed all eleven series in its current TV show lineup for the 2016-17 TV season, including Arrow, The Flash, and so forth.
CBS joined fellow TV networks FOX and The CW in airing its own DC Comics-based TV show in 2015 with Supergirl.
Hence, The CW may ultimately decide it neither needs nor really has room for Supergirl season 2 as part of its programming slate, even if CBS decides to pass on renewing the DC superhero TV show.
Supergirl would (arguably) feel more at home on The CW than CBS.