Simply put: "Private RPs do not include sign-up sheets."
If your RP has a sign-up sheet/thread, then it's not private. A sign-up sheet/thread implies that it is open to all.
Private RPs, and their participants are planned outside of the forum (maybe during a messenger conversation or etc) - and thus, requires no sign-up sheet/thread. You know who's participating already, and you know the story already.
Sorry for being redundant - but I want to get this point across clearly.
Sally and Mark decide to have a Naruto RP, but solely with the two of them. They plan out everything over MSNm and build their characters in the same way. They come to this forum to register their Private RP in this topic - with this method:
[b]RP Name:[/b] The RPs Name
[b]Participants:[/b] Those taking part in the RP
[b]Link:[/b] You put a link to the RP thread here.
End of Example.