For: It's still very early in the show's run, but there's clearly some kind of connection between these partners. Plus, who to better gripe about your crazy job to than someone who goes through the same issues every day?
Against: They're partners, and the stakes are always high in their special Investigative Unit. Do they really need a possible romance to make things even more complicated? It doesn't help that Dick Wolf fans may still be nursing their wounds after SVU's 12-year-long will-they-or-won't-they partners, Benson and Stabler, ended abruptly with no closure whatsoever. Plus, we like Halstead so far, so it would be a shame to have to watch Lindsay's surrogate father, Sgt. Hank Voight, have to rough up the guy for hurting his pseudo daughter.