If you follow any of the storylines in which you have the opportunity to kill Stefan’s dad, you’ve got to do it. Stefan’s dad is a dick and in all versions of this, he’s a terrible father and maybe not even Stefan’s real father. If you don’t kill Stefan’s dad (when prompted) nothing interesting happens. (Though there is one exception noted below.) Anyway, if you smack him with the glass ashtray (which some paths force you to do) he’ll die. In some of these versions, you have the option of burying him or hacking him up. If you bury him, the dogs next door will find the body, and Stefan will go to jail. In some of these versions, Bandersnatch will still get released and in some versions, it won’t.
In any case, if you hack-up the body of the dad, Stefan won’t go to jail, because the dogs won’t find the body.