I have a case on intake right now that involves a baby who dies from shaken baby syndrome. There were two people who were in charge of the child at the time the injuries were received. Both give statements that deny any wrong doing. the boyfriend states he put him in a play pen and came back a couple of minutes later to find the baby not breathing. The mom states that she left to go get food, and came back to find boyfriend with child in arms coming towards her claiming child not breathing. Don't know which one did it, and neither will give a polygraph. Can I charge them both with the murder, and then try them together in the same trial?? Any advice?

You can charge them both. Trying them together may or may not happen. They do appear to have antagonistic defenses (he did it - she did it). Probably gets severed, but they can be indicted if you have the case. And it looks like you do.