Petra may not be guilty of killing Scott on Jane the Virgin, but it's pretty impossible to ever trust her. After Dennis was given Scott's burn book on Jane the Virgin (by Rafael's ex Abbey), the police understandably had to ask Petra about it during "Chapter 58" on March 20. She told the Miami PD she had been hiding Scott's book to save her staff from embarrassment, but she really ripped out a page to protect Rafael's feelings. Since she lied about that aspect of the burn book to the police, does that mean that Petra knows who J.P. is on Jane the Virgin? Dennis mentioned that Scott wrote a lot about "him" in his book and now there's a new mystery to unravel.
When asked about J.P., Petra said she had no idea who he was. While you might be inclined to believe her, Petra always makes it so damn hard since she lied about having the book and ripping out a page. (And you know, she moved Scott's dead body to avoid the police investigating at the Marbella.) But whether or not Petra knows who J.P. is may not really matter if fans can figure out who this person is before the show reveals it.
As Scott ended up dead (well, probably dead — it is Jane the Virgin after all), the identity of J.P. is going to be of major interest to Dennis. There has been a J.D. and a J.J. on Jane the Virgin, but so far, there is no character named J.P. Considering Scott's burn book seemed to be specifically about the Marbella, perhaps the most obvious answer is that J.P. is actually code for two people — Jane and Petra. Besides Alba's crush Jorge, Jane is the only regular character who works at the hotel with a name that starts with J. And Petra is the only person with a P name at the Marbella. Could Scott have been writing about Jane and/or Petra every time he wrote about J.P.? Dennis could have just assumed the initials belonged to one man, but if they do belong to Jane and Petra, I'm not sure discovering who J.P. is will really help the police with their murder investigation.
The other options are that J.P. is a completely new character or code for a different character that has to do with Scott's death. But knowing how much beef Scott had with Jane and Petra, maybe it was just code for them. That might mean that Dennis will be on a wild goose chase trying to discover J.P.'s identity and the series will be no closer to unveiling who killed Scott.