Maggie Sawyer and Alex Danvers have just met days ago, but have already done a lot of romantic stuff: They've fought over a crime scene (Detective Maggie Sawyer from the NCPD Science Division is convinced that the airport is totally within her jurisdiction, but Alex Danvers from the Secret Service is very convincing when she says it's her crime scene if she says so), followed the same lead, where Maggie found out that Alex isn't actually a Fed, but rather DEO. Maggie was also kidnapped, and rescued by Alex and Supergirl (why are they so tight?, Maggie wonders insistently), establishing that they make a good team, fighting together is a lot of fun and also, Maggie's gone to a date with a pretty lady, which Alex (who isn't gay at all) is very neutral about, and also, that the agent actually does care about the detective. Who'd have thunk it.
Now, Maggie has made the romantic proposition of looking at a dead body together (why is Supergirl there too, again? Why are they so tight? This is not jealousy, neither Maggie nor Alex are jealous.) They have a lead and everything, and it's romantic. But it's not a date, because Alex isn't gay and Maggie has a girlfriend. Up and away! Who doesn't love solving a good old-fashioned murder mystery together?