In the U.S. court system, if two people commit the same murder, do they get a joint trial?

Two characters commit a murder. They are eventually arrested in a public location, pinned down, dragged off into separate cop cars due to the convenience of the circumstances, womp womp. They will not end up in the same prison, most especially because they are opposite sexes. So... after the arrest, would they see each other ever again at any point?
The only difference that it will make for my story is this line: "The last they saw of each other was when they were shoved into separate cop cars." There's a time skip after that, then an epilogue involving moping and self-pity and wallowing in emotions in prison (not really but the point is that "they" indeed do not meet up again, for realsies, after some point).

 

Ah, so change nothing. Thanks!