For a murder 1 charge they'd have to have some kind of evidence he either planned it, or intended it (whatever "it" was that was done to kill this poor baby), hurt him bad enough that those injuries caused his death (even if he didn't plan it or intend it), or evidence that this precious little guy died as a result of injuries sustained while daddy was committing another felony against him. Those are listed as:
Kidnapping; Sexual Assault; Arson; Robbery; Burglary; Carjacking; Criminal Escape; Terrorism; Escape. - See more at:
http://statelaws.findlaw.com/new-je...t-degree-murder-law.html#sthash.ZQY95SLy.dpuf
Nine different felonies that net a murder 1 charge if the victim dies while one of those things are being done. Pretty sure we can rule out the last 7. I genuinely hope it's neither of the first two either.
ETA: I haven't followed this case closely but I think I recall sexual assault was ruled out? Or no evidence of it? I do hope that's the case. If so, that rules out the last category that could be applied for 1st degree murder since none of those other things would apply - at least I wouldn't think so.