http://www.hebrewbooks.org/pdfpager.aspx?req=14503&st=&pgnum=92
Its a long siman and I didnt reread it now. I remember him saying that to solve a murder/prevent future murder it is mutar. (though in the summary he doesnt mention this case but does allow in a case where the casue of death is not known and just to give the family ease)
Please someone correct me if I’m wrong
Shaken baby is nut murder per se but it is dangerously close.
Please note: I dont know the specifics in this case and like the op am just adding a source.
ALso please note that like almost every post Joseph has absolutely no clue what he was talking about. For example if there is a choleh lifoneinu who would benefit from an autopsy virtually ALL poskim allow one including the Nodah Byihuda, the Chazon Ish among others (the Binyan Tzion and R’ Moshe are some notable exceptions)